Properties

Label 354.2.e.b.223.2
Level $354$
Weight $2$
Character 354.223
Analytic conductor $2.827$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [354,2,Mod(7,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 354.e (of order \(29\), degree \(28\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.82670423155\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(2\) over \(\Q(\zeta_{29})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 223.2
Character \(\chi\) \(=\) 354.223
Dual form 354.2.e.b.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.647386 - 0.762162i) q^{2} +(-0.796093 + 0.605174i) q^{3} +(-0.161782 + 0.986827i) q^{4} +(0.140789 - 0.265557i) q^{5} +(0.976621 + 0.214970i) q^{6} +(-0.694075 + 0.0754852i) q^{7} +(0.856857 - 0.515554i) q^{8} +(0.267528 - 0.963550i) q^{9} +O(q^{10})\) \(q+(-0.647386 - 0.762162i) q^{2} +(-0.796093 + 0.605174i) q^{3} +(-0.161782 + 0.986827i) q^{4} +(0.140789 - 0.265557i) q^{5} +(0.976621 + 0.214970i) q^{6} +(-0.694075 + 0.0754852i) q^{7} +(0.856857 - 0.515554i) q^{8} +(0.267528 - 0.963550i) q^{9} +(-0.293542 + 0.0646136i) q^{10} +(1.30975 - 0.441306i) q^{11} +(-0.468408 - 0.883512i) q^{12} +(1.02091 + 3.67700i) q^{13} +(0.506866 + 0.480129i) q^{14} +(0.0486267 + 0.296610i) q^{15} +(-0.947653 - 0.319302i) q^{16} +(4.84839 + 0.527294i) q^{17} +(-0.907575 + 0.419889i) q^{18} +(0.200283 + 3.69400i) q^{19} +(0.239281 + 0.181897i) q^{20} +(0.506866 - 0.480129i) q^{21} +(-1.18426 - 0.712546i) q^{22} +(3.07555 + 1.42290i) q^{23} +(-0.370138 + 0.928977i) q^{24} +(2.75524 + 4.06367i) q^{25} +(2.14154 - 3.15854i) q^{26} +(0.370138 + 0.928977i) q^{27} +(0.0377980 - 0.697143i) q^{28} +(2.55869 - 3.01233i) q^{29} +(0.194585 - 0.229083i) q^{30} +(0.0121354 - 0.223824i) q^{31} +(0.370138 + 0.928977i) q^{32} +(-0.775616 + 1.14395i) q^{33} +(-2.73690 - 4.03662i) q^{34} +(-0.0776727 + 0.194944i) q^{35} +(0.907575 + 0.419889i) q^{36} +(3.78404 + 2.27678i) q^{37} +(2.68577 - 2.54410i) q^{38} +(-3.03796 - 2.30940i) q^{39} +(-0.0162725 - 0.300129i) q^{40} +(5.51917 - 2.55344i) q^{41} +(-0.694075 - 0.0754852i) q^{42} +(-1.37218 - 0.462342i) q^{43} +(0.223599 + 1.36389i) q^{44} +(-0.218212 - 0.206702i) q^{45} +(-0.906589 - 3.26524i) q^{46} +(-1.73350 - 3.26973i) q^{47} +(0.947653 - 0.319302i) q^{48} +(-6.36030 + 1.40001i) q^{49} +(1.31347 - 4.73070i) q^{50} +(-4.17888 + 2.51435i) q^{51} +(-3.79372 + 0.412592i) q^{52} +(3.27478 + 0.720834i) q^{53} +(0.468408 - 0.883512i) q^{54} +(0.0672069 - 0.409944i) q^{55} +(-0.555806 + 0.422513i) q^{56} +(-2.39496 - 2.81956i) q^{57} -3.95234 q^{58} +(-6.83631 + 3.50212i) q^{59} -0.300570 q^{60} +(-1.04273 - 1.22760i) q^{61} +(-0.178446 + 0.135651i) q^{62} +(-0.112951 + 0.688970i) q^{63} +(0.468408 - 0.883512i) q^{64} +(1.12018 + 0.246571i) q^{65} +(1.37400 - 0.149431i) q^{66} +(-1.39950 + 0.842053i) q^{67} +(-1.30473 + 4.69921i) q^{68} +(-3.30953 + 0.728483i) q^{69} +(0.198863 - 0.0670047i) q^{70} +(-3.17992 - 5.99796i) q^{71} +(-0.267528 - 0.963550i) q^{72} +(3.29561 + 3.12177i) q^{73} +(-0.714458 - 4.35800i) q^{74} +(-4.65265 - 1.56766i) q^{75} +(-3.67774 - 0.399979i) q^{76} +(-0.875752 + 0.405166i) q^{77} +(0.206599 + 3.81050i) q^{78} +(-8.61555 - 6.54937i) q^{79} +(-0.218212 + 0.206702i) q^{80} +(-0.856857 - 0.515554i) q^{81} +(-5.51917 - 2.55344i) q^{82} +(-2.75870 + 6.92381i) q^{83} +(0.391802 + 0.577865i) q^{84} +(0.822628 - 1.21329i) q^{85} +(0.535953 + 1.34514i) q^{86} +(-0.213976 + 3.94655i) q^{87} +(0.894752 - 1.05338i) q^{88} +(-2.12020 + 2.49609i) q^{89} +(-0.0162725 + 0.300129i) q^{90} +(-0.986148 - 2.47505i) q^{91} +(-1.90173 + 2.80484i) q^{92} +(0.125791 + 0.185528i) q^{93} +(-1.36982 + 3.43798i) q^{94} +(1.00917 + 0.466890i) q^{95} +(-0.856857 - 0.515554i) q^{96} +(7.68744 - 7.28193i) q^{97} +(5.18461 + 3.94123i) q^{98} +(-0.0748253 - 1.38007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{8}{29}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.647386 0.762162i −0.457771 0.538930i
\(3\) −0.796093 + 0.605174i −0.459625 + 0.349397i
\(4\) −0.161782 + 0.986827i −0.0808910 + 0.493413i
\(5\) 0.140789 0.265557i 0.0629629 0.118761i −0.850033 0.526730i \(-0.823418\pi\)
0.912996 + 0.407969i \(0.133763\pi\)
\(6\) 0.976621 + 0.214970i 0.398704 + 0.0877613i
\(7\) −0.694075 + 0.0754852i −0.262336 + 0.0285307i −0.238342 0.971181i \(-0.576604\pi\)
−0.0239940 + 0.999712i \(0.507638\pi\)
\(8\) 0.856857 0.515554i 0.302945 0.182276i
\(9\) 0.267528 0.963550i 0.0891761 0.321183i
\(10\) −0.293542 + 0.0646136i −0.0928263 + 0.0204326i
\(11\) 1.30975 0.441306i 0.394904 0.133059i −0.114841 0.993384i \(-0.536636\pi\)
0.509746 + 0.860325i \(0.329739\pi\)
\(12\) −0.468408 0.883512i −0.135218 0.255048i
\(13\) 1.02091 + 3.67700i 0.283150 + 1.01981i 0.959146 + 0.282910i \(0.0912997\pi\)
−0.675996 + 0.736905i \(0.736286\pi\)
\(14\) 0.506866 + 0.480129i 0.135466 + 0.128320i
\(15\) 0.0486267 + 0.296610i 0.0125554 + 0.0765844i
\(16\) −0.947653 0.319302i −0.236913 0.0798254i
\(17\) 4.84839 + 0.527294i 1.17591 + 0.127888i 0.675137 0.737692i \(-0.264084\pi\)
0.500771 + 0.865580i \(0.333050\pi\)
\(18\) −0.907575 + 0.419889i −0.213918 + 0.0989688i
\(19\) 0.200283 + 3.69400i 0.0459481 + 0.847463i 0.927143 + 0.374709i \(0.122257\pi\)
−0.881194 + 0.472754i \(0.843260\pi\)
\(20\) 0.239281 + 0.181897i 0.0535049 + 0.0406734i
\(21\) 0.506866 0.480129i 0.110607 0.104773i
\(22\) −1.18426 0.712546i −0.252485 0.151915i
\(23\) 3.07555 + 1.42290i 0.641297 + 0.296696i 0.713459 0.700697i \(-0.247128\pi\)
−0.0721614 + 0.997393i \(0.522990\pi\)
\(24\) −0.370138 + 0.928977i −0.0755541 + 0.189627i
\(25\) 2.75524 + 4.06367i 0.551047 + 0.812734i
\(26\) 2.14154 3.15854i 0.419991 0.619440i
\(27\) 0.370138 + 0.928977i 0.0712331 + 0.178782i
\(28\) 0.0377980 0.697143i 0.00714315 0.131748i
\(29\) 2.55869 3.01233i 0.475137 0.559375i −0.471421 0.881908i \(-0.656259\pi\)
0.946558 + 0.322534i \(0.104535\pi\)
\(30\) 0.194585 0.229083i 0.0355261 0.0418246i
\(31\) 0.0121354 0.223824i 0.00217958 0.0401999i −0.997241 0.0742279i \(-0.976351\pi\)
0.999421 + 0.0340280i \(0.0108335\pi\)
\(32\) 0.370138 + 0.928977i 0.0654318 + 0.164221i
\(33\) −0.775616 + 1.14395i −0.135017 + 0.199136i
\(34\) −2.73690 4.03662i −0.469374 0.692275i
\(35\) −0.0776727 + 0.194944i −0.0131291 + 0.0329515i
\(36\) 0.907575 + 0.419889i 0.151263 + 0.0699815i
\(37\) 3.78404 + 2.27678i 0.622092 + 0.374300i 0.791432 0.611258i \(-0.209336\pi\)
−0.169340 + 0.985558i \(0.554164\pi\)
\(38\) 2.68577 2.54410i 0.435689 0.412707i
\(39\) −3.03796 2.30940i −0.486464 0.369800i
\(40\) −0.0162725 0.300129i −0.00257291 0.0474545i
\(41\) 5.51917 2.55344i 0.861950 0.398780i 0.0614477 0.998110i \(-0.480428\pi\)
0.800502 + 0.599330i \(0.204566\pi\)
\(42\) −0.694075 0.0754852i −0.107098 0.0116476i
\(43\) −1.37218 0.462342i −0.209256 0.0705065i 0.212721 0.977113i \(-0.431767\pi\)
−0.421977 + 0.906606i \(0.638664\pi\)
\(44\) 0.223599 + 1.36389i 0.0337088 + 0.205614i
\(45\) −0.218212 0.206702i −0.0325291 0.0308132i
\(46\) −0.906589 3.26524i −0.133669 0.481433i
\(47\) −1.73350 3.26973i −0.252857 0.476938i 0.724292 0.689493i \(-0.242167\pi\)
−0.977149 + 0.212554i \(0.931822\pi\)
\(48\) 0.947653 0.319302i 0.136782 0.0460872i
\(49\) −6.36030 + 1.40001i −0.908615 + 0.200001i
\(50\) 1.31347 4.73070i 0.185753 0.669022i
\(51\) −4.17888 + 2.51435i −0.585160 + 0.352079i
\(52\) −3.79372 + 0.412592i −0.526095 + 0.0572162i
\(53\) 3.27478 + 0.720834i 0.449826 + 0.0990142i 0.434105 0.900862i \(-0.357065\pi\)
0.0157209 + 0.999876i \(0.494996\pi\)
\(54\) 0.468408 0.883512i 0.0637423 0.120231i
\(55\) 0.0672069 0.409944i 0.00906218 0.0552769i
\(56\) −0.555806 + 0.422513i −0.0742727 + 0.0564607i
\(57\) −2.39496 2.81956i −0.317220 0.373460i
\(58\) −3.95234 −0.518968
\(59\) −6.83631 + 3.50212i −0.890012 + 0.455937i
\(60\) −0.300570 −0.0388034
\(61\) −1.04273 1.22760i −0.133508 0.157178i 0.691345 0.722525i \(-0.257018\pi\)
−0.824854 + 0.565346i \(0.808743\pi\)
\(62\) −0.178446 + 0.135651i −0.0226627 + 0.0172277i
\(63\) −0.112951 + 0.688970i −0.0142305 + 0.0868021i
\(64\) 0.468408 0.883512i 0.0585511 0.110439i
\(65\) 1.12018 + 0.246571i 0.138942 + 0.0305834i
\(66\) 1.37400 0.149431i 0.169127 0.0183937i
\(67\) −1.39950 + 0.842053i −0.170977 + 0.102873i −0.598470 0.801145i \(-0.704224\pi\)
0.427493 + 0.904019i \(0.359397\pi\)
\(68\) −1.30473 + 4.69921i −0.158222 + 0.569863i
\(69\) −3.30953 + 0.728483i −0.398421 + 0.0876991i
\(70\) 0.198863 0.0670047i 0.0237687 0.00800860i
\(71\) −3.17992 5.99796i −0.377387 0.711827i 0.619959 0.784634i \(-0.287149\pi\)
−0.997346 + 0.0728068i \(0.976804\pi\)
\(72\) −0.267528 0.963550i −0.0315285 0.113555i
\(73\) 3.29561 + 3.12177i 0.385722 + 0.365375i 0.855851 0.517222i \(-0.173034\pi\)
−0.470129 + 0.882598i \(0.655793\pi\)
\(74\) −0.714458 4.35800i −0.0830541 0.506608i
\(75\) −4.65265 1.56766i −0.537242 0.181018i
\(76\) −3.67774 0.399979i −0.421866 0.0458807i
\(77\) −0.875752 + 0.405166i −0.0998012 + 0.0461730i
\(78\) 0.206599 + 3.81050i 0.0233927 + 0.431454i
\(79\) −8.61555 6.54937i −0.969325 0.736862i −0.00456437 0.999990i \(-0.501453\pi\)
−0.964761 + 0.263128i \(0.915246\pi\)
\(80\) −0.218212 + 0.206702i −0.0243969 + 0.0231099i
\(81\) −0.856857 0.515554i −0.0952064 0.0572838i
\(82\) −5.51917 2.55344i −0.609491 0.281980i
\(83\) −2.75870 + 6.92381i −0.302807 + 0.759987i 0.696301 + 0.717750i \(0.254828\pi\)
−0.999108 + 0.0422374i \(0.986551\pi\)
\(84\) 0.391802 + 0.577865i 0.0427492 + 0.0630503i
\(85\) 0.822628 1.21329i 0.0892266 0.131599i
\(86\) 0.535953 + 1.34514i 0.0577933 + 0.145050i
\(87\) −0.213976 + 3.94655i −0.0229406 + 0.423114i
\(88\) 0.894752 1.05338i 0.0953808 0.112291i
\(89\) −2.12020 + 2.49609i −0.224741 + 0.264585i −0.862963 0.505267i \(-0.831394\pi\)
0.638223 + 0.769852i \(0.279670\pi\)
\(90\) −0.0162725 + 0.300129i −0.00171527 + 0.0316363i
\(91\) −0.986148 2.47505i −0.103376 0.259455i
\(92\) −1.90173 + 2.80484i −0.198269 + 0.292425i
\(93\) 0.125791 + 0.185528i 0.0130440 + 0.0192384i
\(94\) −1.36982 + 3.43798i −0.141286 + 0.354601i
\(95\) 1.00917 + 0.466890i 0.103538 + 0.0479019i
\(96\) −0.856857 0.515554i −0.0874526 0.0526185i
\(97\) 7.68744 7.28193i 0.780541 0.739368i −0.189612 0.981859i \(-0.560723\pi\)
0.970154 + 0.242491i \(0.0779645\pi\)
\(98\) 5.18461 + 3.94123i 0.523724 + 0.398125i
\(99\) −0.0748253 1.38007i −0.00752023 0.138702i
\(100\) −4.45588 + 2.06151i −0.445588 + 0.206151i
\(101\) −9.31499 1.01307i −0.926876 0.100804i −0.367786 0.929911i \(-0.619884\pi\)
−0.559090 + 0.829107i \(0.688849\pi\)
\(102\) 4.62169 + 1.55723i 0.457615 + 0.154188i
\(103\) 2.61161 + 15.9301i 0.257330 + 1.56964i 0.726897 + 0.686747i \(0.240962\pi\)
−0.469567 + 0.882897i \(0.655590\pi\)
\(104\) 2.77047 + 2.62432i 0.271666 + 0.257336i
\(105\) −0.0561402 0.202199i −0.00547873 0.0197326i
\(106\) −1.57066 2.96257i −0.152556 0.287751i
\(107\) −9.94798 + 3.35186i −0.961707 + 0.324037i −0.755996 0.654576i \(-0.772847\pi\)
−0.205711 + 0.978613i \(0.565951\pi\)
\(108\) −0.976621 + 0.214970i −0.0939754 + 0.0206855i
\(109\) 1.13265 4.07943i 0.108488 0.390739i −0.889292 0.457341i \(-0.848802\pi\)
0.997780 + 0.0666019i \(0.0212158\pi\)
\(110\) −0.355953 + 0.214170i −0.0339388 + 0.0204203i
\(111\) −4.39029 + 0.477473i −0.416708 + 0.0453197i
\(112\) 0.681845 + 0.150085i 0.0644283 + 0.0141817i
\(113\) 7.18468 13.5517i 0.675878 1.27484i −0.273852 0.961772i \(-0.588298\pi\)
0.949730 0.313069i \(-0.101357\pi\)
\(114\) −0.598501 + 3.65070i −0.0560548 + 0.341919i
\(115\) 0.810867 0.616405i 0.0756137 0.0574801i
\(116\) 2.55869 + 3.01233i 0.237569 + 0.279687i
\(117\) 3.81609 0.352798
\(118\) 7.09492 + 2.94315i 0.653140 + 0.270939i
\(119\) −3.40495 −0.312131
\(120\) 0.194585 + 0.229083i 0.0177631 + 0.0209123i
\(121\) −7.23633 + 5.50091i −0.657848 + 0.500083i
\(122\) −0.260579 + 1.58946i −0.0235918 + 0.143903i
\(123\) −2.84850 + 5.37284i −0.256840 + 0.484452i
\(124\) 0.218912 + 0.0481861i 0.0196589 + 0.00432724i
\(125\) 2.96108 0.322037i 0.264847 0.0288039i
\(126\) 0.598230 0.359943i 0.0532945 0.0320663i
\(127\) 2.02021 7.27615i 0.179265 0.645653i −0.818229 0.574893i \(-0.805044\pi\)
0.997493 0.0707604i \(-0.0225426\pi\)
\(128\) −0.976621 + 0.214970i −0.0863219 + 0.0190009i
\(129\) 1.37218 0.462342i 0.120814 0.0407070i
\(130\) −0.537265 1.01339i −0.0471213 0.0888801i
\(131\) −1.06715 3.84354i −0.0932377 0.335812i 0.902189 0.431341i \(-0.141959\pi\)
−0.995427 + 0.0955293i \(0.969546\pi\)
\(132\) −1.00340 0.950468i −0.0873345 0.0827277i
\(133\) −0.417854 2.54880i −0.0362325 0.221009i
\(134\) 1.54780 + 0.521515i 0.133710 + 0.0450520i
\(135\) 0.298808 + 0.0324973i 0.0257173 + 0.00279692i
\(136\) 4.42623 2.04779i 0.379546 0.175597i
\(137\) −0.315326 5.81585i −0.0269402 0.496882i −0.980603 0.196005i \(-0.937203\pi\)
0.953663 0.300877i \(-0.0972795\pi\)
\(138\) 2.69777 + 2.05079i 0.229649 + 0.174575i
\(139\) 9.24845 8.76060i 0.784444 0.743064i −0.186479 0.982459i \(-0.559708\pi\)
0.970922 + 0.239395i \(0.0769489\pi\)
\(140\) −0.179810 0.108188i −0.0151967 0.00914354i
\(141\) 3.35878 + 1.55394i 0.282860 + 0.130865i
\(142\) −2.51278 + 6.30661i −0.210868 + 0.529239i
\(143\) 2.95982 + 4.36541i 0.247513 + 0.365054i
\(144\) −0.561187 + 0.827689i −0.0467656 + 0.0689741i
\(145\) −0.439707 1.10358i −0.0365157 0.0916475i
\(146\) 0.245760 4.53278i 0.0203393 0.375136i
\(147\) 4.21614 4.96363i 0.347742 0.409393i
\(148\) −2.85897 + 3.36585i −0.235006 + 0.276671i
\(149\) 0.635626 11.7234i 0.0520725 0.960422i −0.849444 0.527678i \(-0.823063\pi\)
0.901517 0.432744i \(-0.142454\pi\)
\(150\) 1.81725 + 4.56096i 0.148378 + 0.372401i
\(151\) 10.5275 15.5270i 0.856720 1.26357i −0.106354 0.994328i \(-0.533918\pi\)
0.963074 0.269239i \(-0.0867720\pi\)
\(152\) 2.07607 + 3.06198i 0.168392 + 0.248359i
\(153\) 1.80516 4.53060i 0.145938 0.366277i
\(154\) 0.875752 + 0.405166i 0.0705701 + 0.0326492i
\(155\) −0.0577294 0.0347346i −0.00463693 0.00278995i
\(156\) 2.77047 2.62432i 0.221815 0.210114i
\(157\) 7.84280 + 5.96194i 0.625923 + 0.475815i 0.869411 0.494089i \(-0.164498\pi\)
−0.243488 + 0.969904i \(0.578292\pi\)
\(158\) 0.585907 + 10.8064i 0.0466123 + 0.859713i
\(159\) −3.04326 + 1.40796i −0.241346 + 0.111659i
\(160\) 0.298808 + 0.0324973i 0.0236228 + 0.00256914i
\(161\) −2.24207 0.755442i −0.176700 0.0595372i
\(162\) 0.161782 + 0.986827i 0.0127108 + 0.0775324i
\(163\) 2.53053 + 2.39704i 0.198206 + 0.187751i 0.780365 0.625324i \(-0.215033\pi\)
−0.582159 + 0.813075i \(0.697792\pi\)
\(164\) 1.62690 + 5.85957i 0.127040 + 0.457555i
\(165\) 0.194585 + 0.367026i 0.0151484 + 0.0285729i
\(166\) 7.06301 2.37981i 0.548196 0.184709i
\(167\) −5.37592 + 1.18333i −0.416002 + 0.0915689i −0.418039 0.908429i \(-0.637282\pi\)
0.00203752 + 0.999998i \(0.499351\pi\)
\(168\) 0.186780 0.672719i 0.0144104 0.0519014i
\(169\) −1.33889 + 0.805581i −0.102991 + 0.0619678i
\(170\) −1.45728 + 0.158489i −0.111768 + 0.0121555i
\(171\) 3.61294 + 0.795268i 0.276288 + 0.0608157i
\(172\) 0.678246 1.27931i 0.0517158 0.0975463i
\(173\) −0.859232 + 5.24109i −0.0653262 + 0.398472i 0.933842 + 0.357687i \(0.116434\pi\)
−0.999168 + 0.0407857i \(0.987014\pi\)
\(174\) 3.14643 2.39186i 0.238530 0.181326i
\(175\) −2.21909 2.61251i −0.167747 0.197487i
\(176\) −1.38210 −0.104180
\(177\) 3.32295 6.92517i 0.249768 0.520528i
\(178\) 3.27501 0.245473
\(179\) 9.28078 + 10.9262i 0.693678 + 0.816661i 0.990389 0.138306i \(-0.0441659\pi\)
−0.296712 + 0.954967i \(0.595890\pi\)
\(180\) 0.239281 0.181897i 0.0178350 0.0135578i
\(181\) 0.754642 4.60311i 0.0560921 0.342147i −0.943839 0.330406i \(-0.892814\pi\)
0.999931 0.0117408i \(-0.00373730\pi\)
\(182\) −1.24797 + 2.35391i −0.0925054 + 0.174484i
\(183\) 1.57303 + 0.346249i 0.116281 + 0.0255955i
\(184\) 3.36889 0.366389i 0.248358 0.0270106i
\(185\) 1.13737 0.684330i 0.0836208 0.0503130i
\(186\) 0.0599671 0.215982i 0.00439700 0.0158366i
\(187\) 6.58288 1.44900i 0.481388 0.105961i
\(188\) 3.50710 1.18168i 0.255782 0.0861829i
\(189\) −0.327027 0.616839i −0.0237877 0.0448685i
\(190\) −0.297474 1.07141i −0.0215811 0.0777279i
\(191\) −10.3276 9.78281i −0.747278 0.707859i 0.215992 0.976395i \(-0.430702\pi\)
−0.963270 + 0.268536i \(0.913460\pi\)
\(192\) 0.161782 + 0.986827i 0.0116756 + 0.0712181i
\(193\) 18.7261 + 6.30954i 1.34793 + 0.454171i 0.898433 0.439111i \(-0.144706\pi\)
0.449498 + 0.893281i \(0.351603\pi\)
\(194\) −10.5268 1.14485i −0.755777 0.0821957i
\(195\) −1.04099 + 0.481613i −0.0745468 + 0.0344890i
\(196\) −0.352583 6.50301i −0.0251845 0.464501i
\(197\) 1.45090 + 1.10294i 0.103372 + 0.0785816i 0.655584 0.755123i \(-0.272423\pi\)
−0.552211 + 0.833704i \(0.686216\pi\)
\(198\) −1.00340 + 0.950468i −0.0713083 + 0.0675468i
\(199\) −5.12568 3.08402i −0.363349 0.218620i 0.322158 0.946686i \(-0.395592\pi\)
−0.685507 + 0.728066i \(0.740419\pi\)
\(200\) 4.45588 + 2.06151i 0.315079 + 0.145771i
\(201\) 0.604546 1.51730i 0.0426414 0.107022i
\(202\) 5.25827 + 7.75537i 0.369971 + 0.545666i
\(203\) −1.54854 + 2.28392i −0.108686 + 0.160300i
\(204\) −1.80516 4.53060i −0.126386 0.317206i
\(205\) 0.0989568 1.82515i 0.00691144 0.127474i
\(206\) 10.4506 12.3034i 0.728130 0.857221i
\(207\) 2.19384 2.58278i 0.152482 0.179516i
\(208\) 0.206599 3.81050i 0.0143251 0.264210i
\(209\) 1.89251 + 4.74984i 0.130907 + 0.328553i
\(210\) −0.117764 + 0.173689i −0.00812648 + 0.0119857i
\(211\) 11.8455 + 17.4707i 0.815475 + 1.20274i 0.976443 + 0.215776i \(0.0692281\pi\)
−0.160968 + 0.986960i \(0.551462\pi\)
\(212\) −1.24114 + 3.11502i −0.0852418 + 0.213941i
\(213\) 6.16132 + 2.85053i 0.422167 + 0.195315i
\(214\) 8.99485 + 5.41202i 0.614875 + 0.369958i
\(215\) −0.315967 + 0.299300i −0.0215488 + 0.0204121i
\(216\) 0.796093 + 0.605174i 0.0541673 + 0.0411769i
\(217\) 0.00847251 + 0.156266i 0.000575152 + 0.0106080i
\(218\) −3.84245 + 1.77771i −0.260244 + 0.120402i
\(219\) −4.51283 0.490799i −0.304949 0.0331652i
\(220\) 0.393671 + 0.132643i 0.0265413 + 0.00894280i
\(221\) 3.01093 + 18.3658i 0.202537 + 1.23542i
\(222\) 3.20613 + 3.03700i 0.215181 + 0.203830i
\(223\) −0.834067 3.00404i −0.0558533 0.201165i 0.930359 0.366649i \(-0.119495\pi\)
−0.986212 + 0.165484i \(0.947081\pi\)
\(224\) −0.327027 0.616839i −0.0218504 0.0412143i
\(225\) 4.65265 1.56766i 0.310177 0.104511i
\(226\) −14.9799 + 3.29732i −0.996448 + 0.219335i
\(227\) 0.410343 1.47792i 0.0272354 0.0980930i −0.948683 0.316228i \(-0.897584\pi\)
0.975919 + 0.218135i \(0.0699973\pi\)
\(228\) 3.16988 1.90726i 0.209931 0.126311i
\(229\) −16.4332 + 1.78722i −1.08594 + 0.118103i −0.633537 0.773712i \(-0.718398\pi\)
−0.452400 + 0.891815i \(0.649432\pi\)
\(230\) −0.994745 0.218960i −0.0655915 0.0144378i
\(231\) 0.451984 0.852532i 0.0297384 0.0560925i
\(232\) 0.639418 3.90028i 0.0419798 0.256066i
\(233\) −14.8072 + 11.2561i −0.970050 + 0.737413i −0.964912 0.262574i \(-0.915429\pi\)
−0.00513827 + 0.999987i \(0.501636\pi\)
\(234\) −2.47049 2.90848i −0.161501 0.190133i
\(235\) −1.11236 −0.0725621
\(236\) −2.34999 7.31283i −0.152972 0.476025i
\(237\) 10.8223 0.702984
\(238\) 2.20432 + 2.59512i 0.142885 + 0.168217i
\(239\) −21.2261 + 16.1356i −1.37300 + 1.04373i −0.380078 + 0.924955i \(0.624103\pi\)
−0.992922 + 0.118772i \(0.962104\pi\)
\(240\) 0.0486267 0.296610i 0.00313884 0.0191461i
\(241\) −1.41029 + 2.66009i −0.0908448 + 0.171351i −0.924771 0.380525i \(-0.875743\pi\)
0.833926 + 0.551877i \(0.186088\pi\)
\(242\) 8.87729 + 1.95404i 0.570654 + 0.125610i
\(243\) 0.994138 0.108119i 0.0637740 0.00693584i
\(244\) 1.38012 0.830394i 0.0883534 0.0531605i
\(245\) −0.523681 + 1.88613i −0.0334567 + 0.120500i
\(246\) 5.93905 1.30728i 0.378660 0.0833494i
\(247\) −13.3784 + 4.50770i −0.851245 + 0.286818i
\(248\) −0.104995 0.198041i −0.00666718 0.0125756i
\(249\) −1.99393 7.18149i −0.126360 0.455109i
\(250\) −2.16241 2.04834i −0.136763 0.129548i
\(251\) 0.0789541 + 0.481599i 0.00498354 + 0.0303982i 0.989201 0.146564i \(-0.0468213\pi\)
−0.984218 + 0.176962i \(0.943373\pi\)
\(252\) −0.661620 0.222926i −0.0416782 0.0140430i
\(253\) 4.65614 + 0.506386i 0.292729 + 0.0318362i
\(254\) −6.85346 + 3.17075i −0.430024 + 0.198950i
\(255\) 0.0793607 + 1.46372i 0.00496976 + 0.0916618i
\(256\) 0.796093 + 0.605174i 0.0497558 + 0.0378234i
\(257\) 22.0575 20.8940i 1.37591 1.30333i 0.468270 0.883585i \(-0.344877\pi\)
0.907641 0.419747i \(-0.137881\pi\)
\(258\) −1.24071 0.746512i −0.0772434 0.0464758i
\(259\) −2.79827 1.29462i −0.173876 0.0804435i
\(260\) −0.424549 + 1.06554i −0.0263294 + 0.0660818i
\(261\) −2.21800 3.27131i −0.137291 0.202489i
\(262\) −2.23854 + 3.30160i −0.138297 + 0.203974i
\(263\) −7.79692 19.5688i −0.480779 1.20666i −0.946780 0.321880i \(-0.895685\pi\)
0.466001 0.884784i \(-0.345694\pi\)
\(264\) −0.0748253 + 1.38007i −0.00460518 + 0.0849375i
\(265\) 0.652477 0.768155i 0.0400813 0.0471874i
\(266\) −1.67208 + 1.96853i −0.102522 + 0.120698i
\(267\) 0.177306 3.27021i 0.0108509 0.200134i
\(268\) −0.604546 1.51730i −0.0369285 0.0926836i
\(269\) −8.48992 + 12.5217i −0.517639 + 0.763461i −0.993225 0.116209i \(-0.962926\pi\)
0.475586 + 0.879669i \(0.342236\pi\)
\(270\) −0.168676 0.248778i −0.0102653 0.0151402i
\(271\) 6.44960 16.1873i 0.391786 0.983308i −0.592317 0.805705i \(-0.701787\pi\)
0.984102 0.177602i \(-0.0568341\pi\)
\(272\) −4.42623 2.04779i −0.268379 0.124166i
\(273\) 2.28290 + 1.37357i 0.138167 + 0.0831325i
\(274\) −4.22849 + 4.00543i −0.255452 + 0.241977i
\(275\) 5.40199 + 4.10649i 0.325752 + 0.247631i
\(276\) −0.183464 3.38379i −0.0110432 0.203680i
\(277\) −9.03613 + 4.18056i −0.542928 + 0.251185i −0.672130 0.740433i \(-0.734620\pi\)
0.129202 + 0.991618i \(0.458758\pi\)
\(278\) −12.6643 1.37733i −0.759555 0.0826066i
\(279\) −0.212419 0.0715722i −0.0127172 0.00428491i
\(280\) 0.0339496 + 0.207083i 0.00202888 + 0.0123756i
\(281\) −16.7807 15.8955i −1.00105 0.948246i −0.00239070 0.999997i \(-0.500761\pi\)
−0.998660 + 0.0517516i \(0.983520\pi\)
\(282\) −0.990076 3.56593i −0.0589582 0.212348i
\(283\) 12.9362 + 24.4003i 0.768979 + 1.45045i 0.889112 + 0.457690i \(0.151323\pi\)
−0.120133 + 0.992758i \(0.538332\pi\)
\(284\) 6.43340 2.16767i 0.381752 0.128627i
\(285\) −1.08594 + 0.239033i −0.0643255 + 0.0141591i
\(286\) 1.41100 5.08197i 0.0834343 0.300503i
\(287\) −3.63797 + 2.18889i −0.214743 + 0.129206i
\(288\) 0.994138 0.108119i 0.0585801 0.00637097i
\(289\) 6.62631 + 1.45856i 0.389783 + 0.0857977i
\(290\) −0.556448 + 1.04957i −0.0326757 + 0.0616330i
\(291\) −1.71308 + 10.4493i −0.100423 + 0.612551i
\(292\) −3.61381 + 2.74715i −0.211482 + 0.160765i
\(293\) 2.01659 + 2.37411i 0.117810 + 0.138697i 0.817906 0.575352i \(-0.195135\pi\)
−0.700095 + 0.714049i \(0.746859\pi\)
\(294\) −6.51256 −0.379820
\(295\) −0.0324676 + 2.30849i −0.00189034 + 0.134406i
\(296\) 4.41618 0.256685
\(297\) 0.894752 + 1.05338i 0.0519188 + 0.0611235i
\(298\) −9.34666 + 7.10514i −0.541437 + 0.411590i
\(299\) −2.09213 + 12.7615i −0.120991 + 0.738014i
\(300\) 2.29973 4.33774i 0.132775 0.250440i
\(301\) 0.987297 + 0.217321i 0.0569069 + 0.0125261i
\(302\) −18.6495 + 2.02825i −1.07316 + 0.116713i
\(303\) 8.02868 4.83069i 0.461235 0.277516i
\(304\) 0.989702 3.56459i 0.0567633 0.204443i
\(305\) −0.472804 + 0.104072i −0.0270727 + 0.00595914i
\(306\) −4.62169 + 1.55723i −0.264204 + 0.0890208i
\(307\) −2.45034 4.62183i −0.139848 0.263782i 0.803688 0.595051i \(-0.202868\pi\)
−0.943536 + 0.331269i \(0.892523\pi\)
\(308\) −0.258148 0.929764i −0.0147093 0.0529782i
\(309\) −11.7196 11.1014i −0.666705 0.631536i
\(310\) 0.0108998 + 0.0664858i 0.000619067 + 0.00377614i
\(311\) 1.74740 + 0.588768i 0.0990860 + 0.0333860i 0.368408 0.929664i \(-0.379903\pi\)
−0.269322 + 0.963050i \(0.586800\pi\)
\(312\) −3.79372 0.412592i −0.214777 0.0233584i
\(313\) −7.39199 + 3.41990i −0.417820 + 0.193304i −0.617524 0.786552i \(-0.711864\pi\)
0.199704 + 0.979856i \(0.436002\pi\)
\(314\) −0.533355 9.83716i −0.0300990 0.555143i
\(315\) 0.167058 + 0.126995i 0.00941268 + 0.00715533i
\(316\) 7.85694 7.44249i 0.441987 0.418673i
\(317\) −0.244683 0.147221i −0.0137428 0.00826875i 0.508666 0.860964i \(-0.330139\pi\)
−0.522409 + 0.852695i \(0.674966\pi\)
\(318\) 3.04326 + 1.40796i 0.170658 + 0.0789546i
\(319\) 2.02189 5.07456i 0.113204 0.284121i
\(320\) −0.168676 0.248778i −0.00942926 0.0139071i
\(321\) 5.89106 8.68866i 0.328807 0.484954i
\(322\) 0.875718 + 2.19789i 0.0488018 + 0.122483i
\(323\) −0.976777 + 18.0156i −0.0543493 + 1.00241i
\(324\) 0.647386 0.762162i 0.0359659 0.0423423i
\(325\) −12.1292 + 14.2796i −0.672809 + 0.792092i
\(326\) 0.188706 3.48048i 0.0104515 0.192766i
\(327\) 1.56707 + 3.93306i 0.0866594 + 0.217499i
\(328\) 3.41271 5.03336i 0.188435 0.277921i
\(329\) 1.44999 + 2.13858i 0.0799407 + 0.117904i
\(330\) 0.153762 0.385912i 0.00846430 0.0212438i
\(331\) −25.8177 11.9445i −1.41907 0.656531i −0.447717 0.894176i \(-0.647763\pi\)
−0.971352 + 0.237644i \(0.923625\pi\)
\(332\) −6.38630 3.84251i −0.350493 0.210885i
\(333\) 3.20613 3.03700i 0.175695 0.166427i
\(334\) 4.38219 + 3.33125i 0.239783 + 0.182278i
\(335\) 0.0265779 + 0.490200i 0.00145210 + 0.0267825i
\(336\) −0.633639 + 0.293153i −0.0345679 + 0.0159928i
\(337\) −27.0069 2.93718i −1.47116 0.159998i −0.662848 0.748754i \(-0.730653\pi\)
−0.808311 + 0.588755i \(0.799618\pi\)
\(338\) 1.48076 + 0.498926i 0.0805428 + 0.0271380i
\(339\) 2.48149 + 15.1364i 0.134776 + 0.822098i
\(340\) 1.06422 + 1.00808i 0.0577152 + 0.0546708i
\(341\) −0.0828804 0.298508i −0.00448823 0.0161651i
\(342\) −1.73284 3.26849i −0.0937015 0.176740i
\(343\) 8.94019 3.01230i 0.482725 0.162649i
\(344\) −1.41413 + 0.311273i −0.0762446 + 0.0167827i
\(345\) −0.272493 + 0.981431i −0.0146705 + 0.0528385i
\(346\) 4.55081 2.73813i 0.244653 0.147203i
\(347\) 3.17961 0.345804i 0.170691 0.0185637i −0.0223746 0.999750i \(-0.507123\pi\)
0.193065 + 0.981186i \(0.438157\pi\)
\(348\) −3.85994 0.849637i −0.206914 0.0455453i
\(349\) 4.42520 8.34681i 0.236875 0.446794i −0.736365 0.676585i \(-0.763459\pi\)
0.973240 + 0.229790i \(0.0738041\pi\)
\(350\) −0.554550 + 3.38261i −0.0296420 + 0.180808i
\(351\) −3.03796 + 2.30940i −0.162155 + 0.123267i
\(352\) 0.894752 + 1.05338i 0.0476904 + 0.0561455i
\(353\) −19.3797 −1.03148 −0.515740 0.856745i \(-0.672483\pi\)
−0.515740 + 0.856745i \(0.672483\pi\)
\(354\) −7.42933 + 1.95064i −0.394865 + 0.103675i
\(355\) −2.04050 −0.108298
\(356\) −2.12020 2.49609i −0.112370 0.132293i
\(357\) 2.71066 2.06059i 0.143463 0.109058i
\(358\) 2.31927 14.1469i 0.122577 0.747688i
\(359\) 3.05653 5.76523i 0.161318 0.304277i −0.789656 0.613550i \(-0.789741\pi\)
0.950973 + 0.309273i \(0.100086\pi\)
\(360\) −0.293542 0.0646136i −0.0154710 0.00340543i
\(361\) 5.28307 0.574568i 0.278056 0.0302404i
\(362\) −3.99686 + 2.40483i −0.210070 + 0.126395i
\(363\) 2.43178 8.75848i 0.127635 0.459701i
\(364\) 2.60198 0.572739i 0.136381 0.0300197i
\(365\) 1.29299 0.435660i 0.0676784 0.0228035i
\(366\) −0.754457 1.42306i −0.0394361 0.0743844i
\(367\) −8.28291 29.8323i −0.432364 1.55723i −0.783794 0.621021i \(-0.786718\pi\)
0.351430 0.936214i \(-0.385696\pi\)
\(368\) −2.46022 2.33045i −0.128248 0.121483i
\(369\) −0.983833 6.00112i −0.0512163 0.312406i
\(370\) −1.25789 0.423831i −0.0653944 0.0220339i
\(371\) −2.32736 0.253115i −0.120830 0.0131411i
\(372\) −0.203435 + 0.0941191i −0.0105476 + 0.00487985i
\(373\) 1.35663 + 25.0216i 0.0702437 + 1.29557i 0.795019 + 0.606584i \(0.207461\pi\)
−0.724776 + 0.688985i \(0.758057\pi\)
\(374\) −5.36604 4.07916i −0.277471 0.210928i
\(375\) −2.16241 + 2.04834i −0.111666 + 0.105776i
\(376\) −3.17108 1.90798i −0.163536 0.0983963i
\(377\) 13.6885 + 6.33298i 0.704994 + 0.326165i
\(378\) −0.258418 + 0.648581i −0.0132916 + 0.0333594i
\(379\) 5.21568 + 7.69255i 0.267911 + 0.395140i 0.937719 0.347395i \(-0.112934\pi\)
−0.669808 + 0.742535i \(0.733623\pi\)
\(380\) −0.624004 + 0.920337i −0.0320107 + 0.0472123i
\(381\) 2.79506 + 7.01507i 0.143195 + 0.359393i
\(382\) −0.770148 + 14.2046i −0.0394042 + 0.726768i
\(383\) 13.8164 16.2659i 0.705985 0.831149i −0.285904 0.958258i \(-0.592294\pi\)
0.991889 + 0.127109i \(0.0405698\pi\)
\(384\) 0.647386 0.762162i 0.0330368 0.0388939i
\(385\) −0.0157019 + 0.289605i −0.000800244 + 0.0147596i
\(386\) −7.31410 18.3570i −0.372278 0.934347i
\(387\) −0.812588 + 1.19848i −0.0413062 + 0.0609220i
\(388\) 5.94231 + 8.76426i 0.301675 + 0.444938i
\(389\) 10.5518 26.4829i 0.534996 1.34274i −0.374578 0.927195i \(-0.622213\pi\)
0.909574 0.415542i \(-0.136408\pi\)
\(390\) 1.04099 + 0.481613i 0.0527126 + 0.0243874i
\(391\) 14.1612 + 8.52051i 0.716163 + 0.430901i
\(392\) −4.72809 + 4.47869i −0.238805 + 0.226208i
\(393\) 3.17557 + 2.41400i 0.160186 + 0.121770i
\(394\) −0.0986695 1.81985i −0.00497090 0.0916828i
\(395\) −2.95221 + 1.36584i −0.148542 + 0.0687227i
\(396\) 1.37400 + 0.149431i 0.0690459 + 0.00750920i
\(397\) −35.5315 11.9720i −1.78327 0.600855i −0.783486 0.621410i \(-0.786560\pi\)
−0.999789 + 0.0205549i \(0.993457\pi\)
\(398\) 0.967771 + 5.90314i 0.0485100 + 0.295898i
\(399\) 1.87512 + 1.77620i 0.0938732 + 0.0889214i
\(400\) −1.31347 4.73070i −0.0656736 0.236535i
\(401\) −11.3475 21.4036i −0.566666 1.06885i −0.986885 0.161423i \(-0.948392\pi\)
0.420219 0.907423i \(-0.361953\pi\)
\(402\) −1.54780 + 0.521515i −0.0771973 + 0.0260108i
\(403\) 0.835387 0.183883i 0.0416136 0.00915985i
\(404\) 2.50672 9.02838i 0.124714 0.449179i
\(405\) −0.257545 + 0.154960i −0.0127975 + 0.00770001i
\(406\) 2.74322 0.298343i 0.136144 0.0148065i
\(407\) 5.96090 + 1.31209i 0.295471 + 0.0650380i
\(408\) −2.28442 + 4.30887i −0.113096 + 0.213321i
\(409\) −2.09359 + 12.7703i −0.103521 + 0.631453i 0.883196 + 0.469005i \(0.155387\pi\)
−0.986717 + 0.162448i \(0.948061\pi\)
\(410\) −1.45512 + 1.10616i −0.0718635 + 0.0546292i
\(411\) 3.77063 + 4.43913i 0.185992 + 0.218966i
\(412\) −16.1428 −0.795299
\(413\) 4.48055 2.94677i 0.220474 0.145001i
\(414\) −3.38876 −0.166548
\(415\) 1.45027 + 1.70739i 0.0711910 + 0.0838125i
\(416\) −3.03796 + 2.30940i −0.148948 + 0.113228i
\(417\) −2.06094 + 12.5712i −0.100925 + 0.615613i
\(418\) 2.39496 4.51738i 0.117141 0.220952i
\(419\) 16.5220 + 3.63677i 0.807154 + 0.177668i 0.599334 0.800499i \(-0.295432\pi\)
0.207820 + 0.978167i \(0.433363\pi\)
\(420\) 0.208618 0.0226885i 0.0101795 0.00110709i
\(421\) −7.37008 + 4.43443i −0.359196 + 0.216121i −0.683700 0.729764i \(-0.739630\pi\)
0.324504 + 0.945884i \(0.394803\pi\)
\(422\) 5.64695 20.3385i 0.274889 0.990062i
\(423\) −3.61430 + 0.795568i −0.175733 + 0.0386819i
\(424\) 3.17765 1.07067i 0.154320 0.0519966i
\(425\) 11.2157 + 21.1551i 0.544042 + 1.02617i
\(426\) −1.81619 6.54132i −0.0879947 0.316928i
\(427\) 0.816401 + 0.773336i 0.0395084 + 0.0374243i
\(428\) −1.69830 10.3592i −0.0820907 0.500731i
\(429\) −4.99813 1.68406i −0.241312 0.0813074i
\(430\) 0.432667 + 0.0470554i 0.0208651 + 0.00226921i
\(431\) 13.3927 6.19614i 0.645105 0.298457i −0.0699237 0.997552i \(-0.522276\pi\)
0.715029 + 0.699095i \(0.246414\pi\)
\(432\) −0.0541389 0.998533i −0.00260476 0.0480420i
\(433\) 18.9795 + 14.4278i 0.912096 + 0.693357i 0.952082 0.305843i \(-0.0989383\pi\)
−0.0399863 + 0.999200i \(0.512731\pi\)
\(434\) 0.113615 0.107622i 0.00545371 0.00516603i
\(435\) 1.01791 + 0.612454i 0.0488049 + 0.0293649i
\(436\) 3.84245 + 1.77771i 0.184020 + 0.0851367i
\(437\) −4.64023 + 11.6461i −0.221972 + 0.557108i
\(438\) 2.54747 + 3.75724i 0.121723 + 0.179528i
\(439\) 22.0091 32.4611i 1.05044 1.54928i 0.233672 0.972316i \(-0.424926\pi\)
0.816768 0.576967i \(-0.195764\pi\)
\(440\) −0.153762 0.385912i −0.00733030 0.0183977i
\(441\) −0.352583 + 6.50301i −0.0167897 + 0.309667i
\(442\) 12.0485 14.1846i 0.573089 0.674693i
\(443\) −13.8131 + 16.2621i −0.656282 + 0.772635i −0.985142 0.171744i \(-0.945060\pi\)
0.328859 + 0.944379i \(0.393336\pi\)
\(444\) 0.239087 4.40970i 0.0113466 0.209275i
\(445\) 0.364353 + 0.914457i 0.0172720 + 0.0433494i
\(446\) −1.74960 + 2.58047i −0.0828460 + 0.122189i
\(447\) 6.58871 + 9.71761i 0.311635 + 0.459627i
\(448\) −0.258418 + 0.648581i −0.0122091 + 0.0306426i
\(449\) 11.5998 + 5.36663i 0.547428 + 0.253267i 0.674052 0.738684i \(-0.264552\pi\)
−0.126625 + 0.991951i \(0.540414\pi\)
\(450\) −4.20688 2.53119i −0.198314 0.119322i
\(451\) 6.10189 5.78001i 0.287327 0.272170i
\(452\) 12.2109 + 9.28246i 0.574351 + 0.436610i
\(453\) 1.01561 + 18.7319i 0.0477177 + 0.880102i
\(454\) −1.39206 + 0.644038i −0.0653328 + 0.0302262i
\(455\) −0.796104 0.0865816i −0.0373219 0.00405901i
\(456\) −3.50578 1.18123i −0.164173 0.0553163i
\(457\) 2.66782 + 16.2730i 0.124796 + 0.761219i 0.972872 + 0.231345i \(0.0743126\pi\)
−0.848076 + 0.529874i \(0.822239\pi\)
\(458\) 12.0008 + 11.3678i 0.560760 + 0.531180i
\(459\) 1.30473 + 4.69921i 0.0608996 + 0.219341i
\(460\) 0.477101 + 0.899908i 0.0222450 + 0.0419584i
\(461\) 15.8671 5.34626i 0.739006 0.249000i 0.0754740 0.997148i \(-0.475953\pi\)
0.663532 + 0.748148i \(0.269056\pi\)
\(462\) −0.942376 + 0.207433i −0.0438433 + 0.00965064i
\(463\) 4.17617 15.0412i 0.194083 0.699023i −0.800884 0.598820i \(-0.795637\pi\)
0.994967 0.100204i \(-0.0319495\pi\)
\(464\) −3.38659 + 2.03765i −0.157219 + 0.0945953i
\(465\) 0.0669784 0.00728434i 0.00310605 0.000337803i
\(466\) 18.1649 + 3.99841i 0.841475 + 0.185223i
\(467\) 4.97240 9.37895i 0.230095 0.434006i −0.741400 0.671063i \(-0.765838\pi\)
0.971496 + 0.237057i \(0.0761828\pi\)
\(468\) −0.617375 + 3.76582i −0.0285382 + 0.174075i
\(469\) 0.907797 0.690090i 0.0419182 0.0318654i
\(470\) 0.720124 + 0.847796i 0.0332168 + 0.0391059i
\(471\) −9.85161 −0.453938
\(472\) −4.05221 + 6.52530i −0.186518 + 0.300351i
\(473\) −2.00125 −0.0920176
\(474\) −7.00620 8.24834i −0.321806 0.378859i
\(475\) −14.4594 + 10.9917i −0.663442 + 0.504336i
\(476\) 0.550859 3.36009i 0.0252486 0.154010i
\(477\) 1.57066 2.96257i 0.0719154 0.135647i
\(478\) 26.0394 + 5.73171i 1.19102 + 0.262162i
\(479\) 4.30239 0.467913i 0.196581 0.0213795i −0.00929874 0.999957i \(-0.502960\pi\)
0.205880 + 0.978577i \(0.433994\pi\)
\(480\) −0.257545 + 0.154960i −0.0117553 + 0.00707291i
\(481\) −4.50853 + 16.2383i −0.205571 + 0.740402i
\(482\) 2.94042 0.647236i 0.133933 0.0294808i
\(483\) 2.24207 0.755442i 0.102018 0.0343738i
\(484\) −4.25774 8.03095i −0.193534 0.365043i
\(485\) −0.851457 3.06667i −0.0386627 0.139250i
\(486\) −0.725995 0.687699i −0.0329318 0.0311947i
\(487\) −3.32077 20.2558i −0.150479 0.917879i −0.948853 0.315718i \(-0.897755\pi\)
0.798375 0.602161i \(-0.205694\pi\)
\(488\) −1.52637 0.514293i −0.0690954 0.0232810i
\(489\) −3.46516 0.376859i −0.156700 0.0170422i
\(490\) 1.77656 0.821924i 0.0802568 0.0371307i
\(491\) 0.780394 + 14.3935i 0.0352187 + 0.649571i 0.961846 + 0.273590i \(0.0882112\pi\)
−0.926628 + 0.375980i \(0.877306\pi\)
\(492\) −4.84122 3.68020i −0.218259 0.165916i
\(493\) 13.9939 13.2558i 0.630255 0.597009i
\(494\) 12.0966 + 7.27826i 0.544250 + 0.327464i
\(495\) −0.377022 0.174429i −0.0169459 0.00784000i
\(496\) −0.0829673 + 0.208232i −0.00372534 + 0.00934991i
\(497\) 2.65986 + 3.92300i 0.119311 + 0.175970i
\(498\) −4.18262 + 6.16890i −0.187428 + 0.276435i
\(499\) −10.4460 26.2174i −0.467625 1.17365i −0.953975 0.299886i \(-0.903051\pi\)
0.486350 0.873764i \(-0.338328\pi\)
\(500\) −0.161255 + 2.97417i −0.00721154 + 0.133009i
\(501\) 3.56361 4.19541i 0.159211 0.187437i
\(502\) 0.315942 0.371956i 0.0141012 0.0166012i
\(503\) −0.977448 + 18.0280i −0.0435823 + 0.803828i 0.892284 + 0.451474i \(0.149101\pi\)
−0.935867 + 0.352354i \(0.885381\pi\)
\(504\) 0.258418 + 0.648581i 0.0115109 + 0.0288901i
\(505\) −1.58048 + 2.33103i −0.0703303 + 0.103729i
\(506\) −2.62837 3.87656i −0.116846 0.172334i
\(507\) 0.578361 1.45158i 0.0256859 0.0644668i
\(508\) 6.85346 + 3.17075i 0.304073 + 0.140679i
\(509\) 25.3547 + 15.2554i 1.12383 + 0.676185i 0.951130 0.308789i \(-0.0999238\pi\)
0.172698 + 0.984975i \(0.444751\pi\)
\(510\) 1.06422 1.00808i 0.0471243 0.0446385i
\(511\) −2.52305 1.91797i −0.111613 0.0848460i
\(512\) −0.0541389 0.998533i −0.00239262 0.0441294i
\(513\) −3.35751 + 1.55335i −0.148238 + 0.0685821i
\(514\) −30.2044 3.28492i −1.33226 0.144892i
\(515\) 4.59805 + 1.54926i 0.202614 + 0.0682686i
\(516\) 0.234257 + 1.42891i 0.0103126 + 0.0629040i
\(517\) −3.71340 3.51752i −0.163315 0.154700i
\(518\) 0.824852 + 2.97085i 0.0362419 + 0.130532i
\(519\) −2.48774 4.69238i −0.109200 0.205972i
\(520\) 1.08696 0.366239i 0.0476663 0.0160607i
\(521\) −6.59247 + 1.45111i −0.288821 + 0.0635744i −0.357018 0.934097i \(-0.616207\pi\)
0.0681966 + 0.997672i \(0.478276\pi\)
\(522\) −1.05736 + 3.80828i −0.0462796 + 0.166684i
\(523\) −24.8169 + 14.9318i −1.08517 + 0.652923i −0.941605 0.336718i \(-0.890683\pi\)
−0.143561 + 0.989641i \(0.545855\pi\)
\(524\) 3.96555 0.431280i 0.173236 0.0188406i
\(525\) 3.34762 + 0.736868i 0.146102 + 0.0321595i
\(526\) −9.86698 + 18.6111i −0.430221 + 0.811482i
\(527\) 0.176858 1.07879i 0.00770405 0.0469926i
\(528\) 1.10028 0.836410i 0.0478835 0.0364001i
\(529\) −7.45550 8.77730i −0.324152 0.381622i
\(530\) −1.00786 −0.0437788
\(531\) 1.54556 + 7.52404i 0.0670716 + 0.326516i
\(532\) 2.58282 0.111979
\(533\) 15.0236 + 17.6871i 0.650744 + 0.766115i
\(534\) −2.60722 + 1.98195i −0.112825 + 0.0857676i
\(535\) −0.510459 + 3.11366i −0.0220691 + 0.134615i
\(536\) −0.765051 + 1.44304i −0.0330452 + 0.0623298i
\(537\) −14.0006 3.08177i −0.604171 0.132988i
\(538\) 15.0398 1.63568i 0.648412 0.0705191i
\(539\) −7.71257 + 4.64050i −0.332204 + 0.199881i
\(540\) −0.0804109 + 0.289614i −0.00346033 + 0.0124630i
\(541\) −37.3663 + 8.22495i −1.60650 + 0.353618i −0.925525 0.378686i \(-0.876376\pi\)
−0.680978 + 0.732304i \(0.738445\pi\)
\(542\) −16.5127 + 5.56378i −0.709282 + 0.238985i
\(543\) 2.18492 + 4.12119i 0.0937638 + 0.176857i
\(544\) 1.30473 + 4.69921i 0.0559399 + 0.201477i
\(545\) −0.923857 0.875123i −0.0395737 0.0374862i
\(546\) −0.431031 2.62917i −0.0184464 0.112518i
\(547\) 20.8992 + 7.04176i 0.893585 + 0.301084i 0.728378 0.685175i \(-0.240274\pi\)
0.165207 + 0.986259i \(0.447171\pi\)
\(548\) 5.79025 + 0.629728i 0.247347 + 0.0269006i
\(549\) −1.46182 + 0.676308i −0.0623888 + 0.0288641i
\(550\) −0.367367 6.77568i −0.0156646 0.288916i
\(551\) 11.6400 + 8.84850i 0.495881 + 0.376959i
\(552\) −2.46022 + 2.33045i −0.104714 + 0.0991904i
\(553\) 6.47422 + 3.89541i 0.275312 + 0.165650i
\(554\) 9.03613 + 4.18056i 0.383908 + 0.177615i
\(555\) −0.491310 + 1.23310i −0.0208550 + 0.0523420i
\(556\) 7.14896 + 10.5439i 0.303183 + 0.447162i
\(557\) 14.7240 21.7162i 0.623874 0.920145i −0.376105 0.926577i \(-0.622737\pi\)
0.999979 + 0.00643177i \(0.00204731\pi\)
\(558\) 0.0829673 + 0.208232i 0.00351229 + 0.00881518i
\(559\) 0.299151 5.51752i 0.0126528 0.233366i
\(560\) 0.135853 0.159938i 0.00574082 0.00675862i
\(561\) −4.36369 + 5.13733i −0.184235 + 0.216898i
\(562\) −1.25137 + 23.0801i −0.0527857 + 0.973576i
\(563\) 6.34267 + 15.9189i 0.267312 + 0.670901i 0.999953 0.00971362i \(-0.00309199\pi\)
−0.732641 + 0.680615i \(0.761713\pi\)
\(564\) −2.07686 + 3.06313i −0.0874514 + 0.128981i
\(565\) −2.58723 3.81588i −0.108846 0.160535i
\(566\) 10.2223 25.6559i 0.429674 1.07840i
\(567\) 0.633639 + 0.293153i 0.0266104 + 0.0123113i
\(568\) −5.81701 3.49998i −0.244076 0.146856i
\(569\) 22.5765 21.3856i 0.946455 0.896530i −0.0482984 0.998833i \(-0.515380\pi\)
0.994753 + 0.102303i \(0.0326212\pi\)
\(570\) 0.885204 + 0.672915i 0.0370771 + 0.0281853i
\(571\) 0.466502 + 8.60412i 0.0195225 + 0.360071i 0.991930 + 0.126784i \(0.0404655\pi\)
−0.972408 + 0.233287i \(0.925052\pi\)
\(572\) −4.78675 + 2.21459i −0.200144 + 0.0925965i
\(573\) 14.1420 + 1.53804i 0.590792 + 0.0642525i
\(574\) 4.02346 + 1.35566i 0.167936 + 0.0565843i
\(575\) 2.69167 + 16.4185i 0.112250 + 0.684698i
\(576\) −0.725995 0.687699i −0.0302498 0.0286541i
\(577\) −2.99344 10.7814i −0.124619 0.448836i 0.874742 0.484589i \(-0.161031\pi\)
−0.999361 + 0.0357533i \(0.988617\pi\)
\(578\) −3.17812 5.99458i −0.132192 0.249341i
\(579\) −18.7261 + 6.30954i −0.778228 + 0.262216i
\(580\) 1.16018 0.255375i 0.0481739 0.0106039i
\(581\) 1.39210 5.01388i 0.0577540 0.208011i
\(582\) 9.07311 5.45911i 0.376093 0.226287i
\(583\) 4.60726 0.501069i 0.190813 0.0207522i
\(584\) 4.43331 + 0.975845i 0.183452 + 0.0403807i
\(585\) 0.537265 1.01339i 0.0222132 0.0418985i
\(586\) 0.503945 3.07393i 0.0208178 0.126983i
\(587\) 32.7931 24.9287i 1.35352 1.02892i 0.358061 0.933698i \(-0.383438\pi\)
0.995456 0.0952191i \(-0.0303552\pi\)
\(588\) 4.21614 + 4.96363i 0.173871 + 0.204697i
\(589\) 0.829236 0.0341681
\(590\) 1.78046 1.46974i 0.0733005 0.0605082i
\(591\) −1.82252 −0.0749686
\(592\) −2.85897 3.36585i −0.117503 0.138335i
\(593\) −27.0905 + 20.5937i −1.11247 + 0.845681i −0.989183 0.146689i \(-0.953138\pi\)
−0.123292 + 0.992370i \(0.539345\pi\)
\(594\) 0.223599 1.36389i 0.00917436 0.0559611i
\(595\) −0.479380 + 0.904207i −0.0196527 + 0.0370689i
\(596\) 11.4662 + 2.52389i 0.469673 + 0.103383i
\(597\) 5.94688 0.646762i 0.243390 0.0264702i
\(598\) 11.0807 6.66705i 0.453124 0.272636i
\(599\) 10.5541 38.0123i 0.431227 1.55314i −0.354797 0.934943i \(-0.615450\pi\)
0.786024 0.618196i \(-0.212136\pi\)
\(600\) −4.79487 + 1.05543i −0.195750 + 0.0430878i
\(601\) −17.6019 + 5.93076i −0.717995 + 0.241921i −0.654501 0.756061i \(-0.727121\pi\)
−0.0634947 + 0.997982i \(0.520225\pi\)
\(602\) −0.473529 0.893171i −0.0192996 0.0364029i
\(603\) 0.436954 + 1.57376i 0.0177941 + 0.0640887i
\(604\) 13.6193 + 12.9008i 0.554160 + 0.524928i
\(605\) 0.442008 + 2.69613i 0.0179702 + 0.109613i
\(606\) −8.87943 2.99183i −0.360702 0.121535i
\(607\) 8.95047 + 0.973422i 0.363288 + 0.0395100i 0.287943 0.957648i \(-0.407029\pi\)
0.0753453 + 0.997158i \(0.475994\pi\)
\(608\) −3.35751 + 1.55335i −0.136165 + 0.0629967i
\(609\) −0.149391 2.75535i −0.00605362 0.111652i
\(610\) 0.385406 + 0.292978i 0.0156046 + 0.0118623i
\(611\) 10.2530 9.71217i 0.414793 0.392912i
\(612\) 4.17888 + 2.51435i 0.168921 + 0.101636i
\(613\) −30.3874 14.0587i −1.22734 0.567826i −0.304314 0.952572i \(-0.598427\pi\)
−0.923023 + 0.384746i \(0.874289\pi\)
\(614\) −1.93627 + 4.85967i −0.0781414 + 0.196120i
\(615\) 1.02576 + 1.51288i 0.0413625 + 0.0610051i
\(616\) −0.541510 + 0.798667i −0.0218180 + 0.0321792i
\(617\) −18.0012 45.1795i −0.724699 1.81886i −0.551919 0.833898i \(-0.686104\pi\)
−0.172780 0.984960i \(-0.555275\pi\)
\(618\) −0.873954 + 16.1191i −0.0351556 + 0.648406i
\(619\) 23.9305 28.1732i 0.961849 1.13238i −0.0292928 0.999571i \(-0.509326\pi\)
0.991142 0.132806i \(-0.0423986\pi\)
\(620\) 0.0436166 0.0513494i 0.00175168 0.00206224i
\(621\) −0.183464 + 3.38379i −0.00736215 + 0.135787i
\(622\) −0.682507 1.71296i −0.0273660 0.0686836i
\(623\) 1.28316 1.89252i 0.0514087 0.0758221i
\(624\) 2.14154 + 3.15854i 0.0857303 + 0.126443i
\(625\) −8.75489 + 21.9731i −0.350196 + 0.878925i
\(626\) 7.39199 + 3.41990i 0.295443 + 0.136687i
\(627\) −4.38109 2.63601i −0.174964 0.105272i
\(628\) −7.15222 + 6.77495i −0.285405 + 0.270350i
\(629\) 17.1460 + 13.0340i 0.683654 + 0.519700i
\(630\) −0.0113609 0.209540i −0.000452630 0.00834828i
\(631\) −1.25424 + 0.580271i −0.0499303 + 0.0231002i −0.444695 0.895682i \(-0.646688\pi\)
0.394765 + 0.918782i \(0.370826\pi\)
\(632\) −10.7589 1.17010i −0.427964 0.0465439i
\(633\) −20.0029 6.73977i −0.795045 0.267882i
\(634\) 0.0461983 + 0.281797i 0.00183477 + 0.0111916i
\(635\) −1.64781 1.56088i −0.0653912 0.0619418i
\(636\) −0.897070 3.23096i −0.0355711 0.128116i
\(637\) −11.6411 21.9575i −0.461239 0.869988i
\(638\) −5.17658 + 1.74419i −0.204943 + 0.0690533i
\(639\) −6.63006 + 1.45939i −0.262281 + 0.0577324i
\(640\) −0.0804109 + 0.289614i −0.00317852 + 0.0114480i
\(641\) 5.55968 3.34515i 0.219594 0.132125i −0.401507 0.915856i \(-0.631513\pi\)
0.621101 + 0.783731i \(0.286686\pi\)
\(642\) −10.4360 + 1.13498i −0.411874 + 0.0447940i
\(643\) 36.3577 + 8.00294i 1.43381 + 0.315605i 0.862886 0.505399i \(-0.168655\pi\)
0.570922 + 0.821004i \(0.306586\pi\)
\(644\) 1.10822 2.09032i 0.0436699 0.0823701i
\(645\) 0.0704106 0.429485i 0.00277241 0.0169110i
\(646\) 14.3631 10.9186i 0.565110 0.429586i
\(647\) 0.700391 + 0.824564i 0.0275352 + 0.0324170i 0.775757 0.631031i \(-0.217368\pi\)
−0.748222 + 0.663448i \(0.769092\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −7.40835 + 7.60381i −0.290803 + 0.298476i
\(650\) 18.7357 0.734875
\(651\) −0.101313 0.119275i −0.00397078 0.00467476i
\(652\) −2.77486 + 2.10939i −0.108672 + 0.0826102i
\(653\) 3.12193 19.0429i 0.122170 0.745207i −0.852694 0.522410i \(-0.825033\pi\)
0.974865 0.222797i \(-0.0715187\pi\)
\(654\) 1.98313 3.74057i 0.0775464 0.146268i
\(655\) −1.17092 0.257740i −0.0457517 0.0100707i
\(656\) −6.04558 + 0.657496i −0.236040 + 0.0256709i
\(657\) 3.88965 2.34032i 0.151750 0.0913047i
\(658\) 0.691239 2.48962i 0.0269473 0.0970554i
\(659\) −11.8870 + 2.61653i −0.463052 + 0.101925i −0.440368 0.897817i \(-0.645152\pi\)
−0.0226836 + 0.999743i \(0.507221\pi\)
\(660\) −0.393671 + 0.132643i −0.0153236 + 0.00516313i
\(661\) −15.7153 29.6422i −0.611254 1.15295i −0.975158 0.221511i \(-0.928901\pi\)
0.363903 0.931437i \(-0.381444\pi\)
\(662\) 7.61035 + 27.4100i 0.295785 + 1.06532i
\(663\) −13.5115 12.7988i −0.524743 0.497063i
\(664\) 1.20579 + 7.35498i 0.0467936 + 0.285428i
\(665\) −0.735680 0.247879i −0.0285284 0.00961235i
\(666\) −4.39029 0.477473i −0.170120 0.0185017i
\(667\) 12.1556 5.62380i 0.470669 0.217754i
\(668\) −0.298014 5.49655i −0.0115305 0.212668i
\(669\) 2.48196 + 1.88674i 0.0959582 + 0.0729455i
\(670\) 0.356406 0.337605i 0.0137691 0.0130428i
\(671\) −1.90747 1.14769i −0.0736370 0.0443059i
\(672\) 0.633639 + 0.293153i 0.0244432 + 0.0113086i
\(673\) −3.76954 + 9.46084i −0.145305 + 0.364689i −0.983558 0.180594i \(-0.942198\pi\)
0.838253 + 0.545282i \(0.183577\pi\)
\(674\) 15.2453 + 22.4851i 0.587227 + 0.866095i
\(675\) −2.75524 + 4.06367i −0.106049 + 0.156411i
\(676\) −0.578361 1.45158i −0.0222447 0.0558299i
\(677\) −1.03120 + 19.0194i −0.0396322 + 0.730974i 0.909425 + 0.415869i \(0.136522\pi\)
−0.949057 + 0.315105i \(0.897960\pi\)
\(678\) 9.92993 11.6904i 0.381357 0.448968i
\(679\) −4.78598 + 5.63449i −0.183669 + 0.216232i
\(680\) 0.0793607 1.46372i 0.00304334 0.0561312i
\(681\) 0.567728 + 1.42489i 0.0217554 + 0.0546019i
\(682\) −0.173856 + 0.256419i −0.00665729 + 0.00981877i
\(683\) −11.9419 17.6129i −0.456942 0.673939i 0.527519 0.849543i \(-0.323122\pi\)
−0.984461 + 0.175604i \(0.943812\pi\)
\(684\) −1.36930 + 3.43668i −0.0523565 + 0.131405i
\(685\) −1.58883 0.735073i −0.0607062 0.0280857i
\(686\) −8.08362 4.86375i −0.308634 0.185699i
\(687\) 12.0008 11.3678i 0.457859 0.433707i
\(688\) 1.15273 + 0.876280i 0.0439473 + 0.0334079i
\(689\) 0.692763 + 12.7773i 0.0263922 + 0.486775i
\(690\) 0.924418 0.427681i 0.0351920 0.0162816i
\(691\) −6.84119 0.744024i −0.260251 0.0283040i −0.0229368 0.999737i \(-0.507302\pi\)
−0.237314 + 0.971433i \(0.576267\pi\)
\(692\) −5.03303 1.69583i −0.191327 0.0644657i
\(693\) 0.156109 + 0.952224i 0.00593010 + 0.0361720i
\(694\) −2.32200 2.19951i −0.0881418 0.0834923i
\(695\) −1.02435 3.68939i −0.0388560 0.139946i
\(696\) 1.85131 + 3.49194i 0.0701738 + 0.132362i
\(697\) 28.1055 9.46985i 1.06457 0.358696i
\(698\) −9.22643 + 2.03089i −0.349226 + 0.0768704i
\(699\) 4.97597 17.9218i 0.188209 0.677866i
\(700\) 2.93710 1.76720i 0.111012 0.0667937i
\(701\) −45.3329 + 4.93024i −1.71220 + 0.186213i −0.911062 0.412269i \(-0.864736\pi\)
−0.801136 + 0.598482i \(0.795771\pi\)
\(702\) 3.72687 + 0.820347i 0.140662 + 0.0309620i
\(703\) −7.65255 + 14.4342i −0.288621 + 0.544398i
\(704\) 0.223599 1.36389i 0.00842719 0.0514036i
\(705\) 0.885539 0.673169i 0.0333513 0.0253530i
\(706\) 12.5462 + 14.7705i 0.472181 + 0.555895i
\(707\) 6.54177 0.246028
\(708\) 6.29635 + 4.39954i 0.236631 + 0.165345i
\(709\) −31.4576 −1.18141 −0.590707 0.806886i \(-0.701151\pi\)
−0.590707 + 0.806886i \(0.701151\pi\)
\(710\) 1.32099 + 1.55519i 0.0495759 + 0.0583653i
\(711\) −8.61555 + 6.54937i −0.323108 + 0.245621i
\(712\) −0.529838 + 3.23187i −0.0198565 + 0.121119i
\(713\) 0.355802 0.671114i 0.0133249 0.0251334i
\(714\) −3.32534 0.731963i −0.124448 0.0273930i
\(715\) 1.57598 0.171398i 0.0589381 0.00640991i
\(716\) −12.2837 + 7.39086i −0.459064 + 0.276209i
\(717\) 7.13305 25.6909i 0.266389 0.959445i
\(718\) −6.37280 + 1.40276i −0.237831 + 0.0523505i
\(719\) 19.4938 6.56824i 0.726997 0.244954i 0.0686210 0.997643i \(-0.478140\pi\)
0.658376 + 0.752689i \(0.271244\pi\)
\(720\) 0.140789 + 0.265557i 0.00524691 + 0.00989672i
\(721\) −3.01514 10.8596i −0.112290 0.404431i
\(722\) −3.85810 3.65459i −0.143584 0.136010i
\(723\) −0.487095 2.97115i −0.0181153 0.110498i
\(724\) 4.42038 + 1.48940i 0.164282 + 0.0553531i
\(725\) 19.2909 + 2.09801i 0.716446 + 0.0779182i
\(726\) −8.24968 + 3.81671i −0.306174 + 0.141651i
\(727\) 0.0563703 + 1.03969i 0.00209066 + 0.0385599i 0.999393 0.0348489i \(-0.0110950\pi\)
−0.997302 + 0.0734088i \(0.976612\pi\)
\(728\) −2.12101 1.61235i −0.0786098 0.0597576i
\(729\) −0.725995 + 0.687699i −0.0268887 + 0.0254704i
\(730\) −1.16911 0.703430i −0.0432707 0.0260351i
\(731\) −6.40909 2.96516i −0.237049 0.109670i
\(732\) −0.596175 + 1.49629i −0.0220353 + 0.0553043i
\(733\) 14.7721 + 21.7871i 0.545618 + 0.804727i 0.996116 0.0880509i \(-0.0280638\pi\)
−0.450498 + 0.892778i \(0.648753\pi\)
\(734\) −17.3748 + 25.6260i −0.641317 + 0.945871i
\(735\) −0.724537 1.81845i −0.0267250 0.0670746i
\(736\) −0.183464 + 3.38379i −0.00676256 + 0.124728i
\(737\) −1.46140 + 1.72049i −0.0538312 + 0.0633750i
\(738\) −3.93690 + 4.63488i −0.144919 + 0.170612i
\(739\) 0.0238028 0.439016i 0.000875599 0.0161495i −0.998063 0.0622119i \(-0.980185\pi\)
0.998939 + 0.0460624i \(0.0146673\pi\)
\(740\) 0.491310 + 1.23310i 0.0180609 + 0.0453295i
\(741\) 7.92248 11.6848i 0.291040 0.429251i
\(742\) 1.31378 + 1.93769i 0.0482305 + 0.0711347i
\(743\) 16.3692 41.0835i 0.600527 1.50721i −0.242947 0.970040i \(-0.578114\pi\)
0.843474 0.537170i \(-0.180507\pi\)
\(744\) 0.203435 + 0.0941191i 0.00745829 + 0.00345057i
\(745\) −3.02375 1.81933i −0.110782 0.0666551i
\(746\) 18.1922 17.2326i 0.666065 0.630931i
\(747\) 5.93341 + 4.51046i 0.217092 + 0.165029i
\(748\) 0.364922 + 6.73058i 0.0133429 + 0.246094i
\(749\) 6.65162 3.07737i 0.243045 0.112445i
\(750\) 2.96108 + 0.322037i 0.108123 + 0.0117591i
\(751\) −30.8288 10.3874i −1.12496 0.379043i −0.305508 0.952190i \(-0.598826\pi\)
−0.819453 + 0.573146i \(0.805723\pi\)
\(752\) 0.598727 + 3.65207i 0.0218333 + 0.133177i
\(753\) −0.354306 0.335616i −0.0129116 0.0122305i
\(754\) −4.03500 14.5327i −0.146946 0.529251i
\(755\) −2.64113 4.98169i −0.0961204 0.181302i
\(756\) 0.661620 0.222926i 0.0240629 0.00810774i
\(757\) −31.0442 + 6.83335i −1.12832 + 0.248362i −0.739635 0.673008i \(-0.765002\pi\)
−0.388686 + 0.921370i \(0.627071\pi\)
\(758\) 2.48641 8.95524i 0.0903105 0.325269i
\(759\) −4.01318 + 2.41465i −0.145669 + 0.0876461i
\(760\) 1.10542 0.120221i 0.0400977 0.00436089i
\(761\) −49.7148 10.9431i −1.80216 0.396685i −0.818180 0.574962i \(-0.805017\pi\)
−0.983980 + 0.178277i \(0.942948\pi\)
\(762\) 3.53714 6.67175i 0.128137 0.241692i
\(763\) −0.478206 + 2.91693i −0.0173122 + 0.105600i
\(764\) 11.3248 8.60885i 0.409715 0.311457i
\(765\) −0.948985 1.11723i −0.0343106 0.0403936i
\(766\) −21.3418 −0.771111
\(767\) −19.8566 21.5617i −0.716979 0.778549i
\(768\) −1.00000 −0.0360844
\(769\) 29.1145 + 34.2762i 1.04989 + 1.23603i 0.970983 + 0.239149i \(0.0768685\pi\)
0.0789111 + 0.996882i \(0.474856\pi\)
\(770\) 0.230891 0.175519i 0.00832074 0.00632526i
\(771\) −4.91534 + 29.9822i −0.177022 + 1.07978i
\(772\) −9.25596 + 17.4586i −0.333129 + 0.628349i
\(773\) −31.1682 6.86063i −1.12104 0.246760i −0.384482 0.923133i \(-0.625620\pi\)
−0.736559 + 0.676373i \(0.763551\pi\)
\(774\) 1.43949 0.156554i 0.0517415 0.00562722i
\(775\) 0.942981 0.567373i 0.0338729 0.0203806i
\(776\) 2.83281 10.2029i 0.101692 0.366261i
\(777\) 3.01115 0.662804i 0.108024 0.0237780i
\(778\) −27.0153 + 9.10253i −0.968547 + 0.326341i
\(779\) 10.5378 + 19.8764i 0.377556 + 0.712147i
\(780\) −0.306855 1.10519i −0.0109872 0.0395723i
\(781\) −6.81184 6.45251i −0.243747 0.230889i
\(782\) −2.67376 16.3092i −0.0956134 0.583216i
\(783\) 3.74545 + 1.26199i 0.133851 + 0.0450998i
\(784\) 6.47439 + 0.704132i 0.231228 + 0.0251476i
\(785\) 2.68742 1.24333i 0.0959180 0.0443764i
\(786\) −0.215957 3.98309i −0.00770292 0.142072i
\(787\) 8.82169 + 6.70607i 0.314459 + 0.239046i 0.750483 0.660889i \(-0.229821\pi\)
−0.436024 + 0.899935i \(0.643614\pi\)
\(788\) −1.32314 + 1.25335i −0.0471351 + 0.0446487i
\(789\) 18.0496 + 10.8601i 0.642583 + 0.386630i
\(790\) 2.95221 + 1.36584i 0.105035 + 0.0485943i
\(791\) −3.96375 + 9.94826i −0.140935 + 0.353719i
\(792\) −0.775616 1.14395i −0.0275603 0.0406484i
\(793\) 3.44934 5.08740i 0.122490 0.180659i
\(794\) 13.8780 + 34.8312i 0.492513 + 1.23611i
\(795\) −0.0545646 + 1.00639i −0.00193521 + 0.0356928i
\(796\) 3.87263 4.55921i 0.137262 0.161597i
\(797\) −0.514612 + 0.605848i −0.0182285 + 0.0214602i −0.771201 0.636592i \(-0.780344\pi\)
0.752972 + 0.658052i \(0.228619\pi\)
\(798\) 0.139831 2.57903i 0.00494997 0.0912968i
\(799\) −6.68057 16.7670i −0.236342 0.593173i
\(800\) −2.75524 + 4.06367i −0.0974123 + 0.143672i
\(801\) 1.83790 + 2.71069i 0.0649389 + 0.0957776i
\(802\) −8.96683 + 22.5050i −0.316630 + 0.794680i
\(803\) 5.69408 + 2.63436i 0.200940 + 0.0929646i
\(804\) 1.39950 + 0.842053i 0.0493567 + 0.0296969i
\(805\) −0.516273 + 0.489039i −0.0181962 + 0.0172364i
\(806\) −0.680967 0.517657i −0.0239860 0.0182337i
\(807\) −0.819040 15.1063i −0.0288316 0.531767i
\(808\) −8.50390 + 3.93432i −0.299166 + 0.138409i
\(809\) −31.1697 3.38991i −1.09587 0.119183i −0.457720 0.889097i \(-0.651334\pi\)
−0.638148 + 0.769914i \(0.720299\pi\)
\(810\) 0.284836 + 0.0959723i 0.0100081 + 0.00337212i
\(811\) 7.10682 + 43.3497i 0.249554 + 1.52221i 0.752904 + 0.658131i \(0.228653\pi\)
−0.503349 + 0.864083i \(0.667899\pi\)
\(812\) −2.00331 1.89764i −0.0703024 0.0665940i
\(813\) 4.66164 + 16.7897i 0.163491 + 0.588841i
\(814\) −2.85898 5.39260i −0.100207 0.189011i
\(815\) 0.992822 0.334521i 0.0347770 0.0117177i
\(816\) 4.76296 1.04841i 0.166737 0.0367016i
\(817\) 1.43307 5.16145i 0.0501367 0.180576i
\(818\) 11.0884 6.67169i 0.387698 0.233270i
\(819\) −2.64865 + 0.288058i −0.0925514 + 0.0100656i
\(820\) 1.78510 + 0.392930i 0.0623383 + 0.0137217i
\(821\) −0.946157 + 1.78464i −0.0330211 + 0.0622844i −0.899474 0.436975i \(-0.856050\pi\)
0.866452 + 0.499260i \(0.166395\pi\)
\(822\) 0.942283 5.74767i 0.0328659 0.200473i
\(823\) 6.12444 4.65568i 0.213485 0.162287i −0.492967 0.870048i \(-0.664088\pi\)
0.706452 + 0.707761i \(0.250295\pi\)
\(824\) 10.4506 + 12.3034i 0.364065 + 0.428610i
\(825\) −6.78563 −0.236245
\(826\) −5.14657 1.50721i −0.179072 0.0524424i
\(827\) −42.2345 −1.46864 −0.734319 0.678805i \(-0.762498\pi\)
−0.734319 + 0.678805i \(0.762498\pi\)
\(828\) 2.19384 + 2.58278i 0.0762411 + 0.0897579i
\(829\) 29.8093 22.6604i 1.03532 0.787029i 0.0578966 0.998323i \(-0.481561\pi\)
0.977423 + 0.211293i \(0.0677675\pi\)
\(830\) 0.362423 2.21068i 0.0125799 0.0767339i
\(831\) 4.66363 8.79654i 0.161780 0.305149i
\(832\) 3.72687 + 0.820347i 0.129206 + 0.0284404i
\(833\) −31.5755 + 3.43404i −1.09402 + 0.118982i
\(834\) 10.9155 6.56764i 0.377973 0.227419i
\(835\) −0.442631 + 1.59421i −0.0153179 + 0.0551700i
\(836\) −4.99344 + 1.09914i −0.172702 + 0.0380145i
\(837\) 0.212419 0.0715722i 0.00734226 0.00247390i
\(838\) −7.92432 14.9469i −0.273741 0.516331i
\(839\) −1.84068 6.62953i −0.0635474 0.228877i 0.924956 0.380073i \(-0.124101\pi\)
−0.988504 + 0.151196i \(0.951687\pi\)
\(840\) −0.152349 0.144312i −0.00525653 0.00497925i
\(841\) 2.16448 + 13.2027i 0.0746372 + 0.455267i
\(842\) 8.15104 + 2.74640i 0.280903 + 0.0946474i
\(843\) 22.9785 + 2.49906i 0.791422 + 0.0860723i
\(844\) −19.1570 + 8.86296i −0.659410 + 0.305076i
\(845\) 0.0254267 + 0.468968i 0.000874705 + 0.0161330i
\(846\) 2.94620 + 2.23965i 0.101293 + 0.0770006i
\(847\) 4.60732 4.36428i 0.158309 0.149958i
\(848\) −2.87319 1.72874i −0.0986659 0.0593653i
\(849\) −25.0649 11.5962i −0.860225 0.397982i
\(850\) 8.86270 22.2437i 0.303988 0.762953i
\(851\) 8.39837 + 12.3867i 0.287893 + 0.424610i
\(852\) −3.80977 + 5.61899i −0.130521 + 0.192504i
\(853\) −15.3061 38.4153i −0.524070 1.31532i −0.918148 0.396239i \(-0.870315\pi\)
0.394078 0.919077i \(-0.371064\pi\)
\(854\) 0.0608806 1.12288i 0.00208329 0.0384240i
\(855\) 0.719852 0.847475i 0.0246184 0.0289830i
\(856\) −6.79593 + 8.00079i −0.232280 + 0.273461i
\(857\) −0.894373 + 16.4957i −0.0305512 + 0.563484i 0.942686 + 0.333681i \(0.108291\pi\)
−0.973237 + 0.229803i \(0.926192\pi\)
\(858\) 1.95219 + 4.89962i 0.0666466 + 0.167270i
\(859\) −4.01215 + 5.91748i −0.136893 + 0.201902i −0.889956 0.456046i \(-0.849265\pi\)
0.753063 + 0.657948i \(0.228575\pi\)
\(860\) −0.244239 0.360226i −0.00832849 0.0122836i
\(861\) 1.57150 3.94417i 0.0535566 0.134417i
\(862\) −13.3927 6.19614i −0.456158 0.211041i
\(863\) −44.7714 26.9381i −1.52404 0.916983i −0.997776 0.0666598i \(-0.978766\pi\)
−0.526261 0.850323i \(-0.676407\pi\)
\(864\) −0.725995 + 0.687699i −0.0246989 + 0.0233960i
\(865\) 1.27084 + 0.966064i 0.0432097 + 0.0328472i
\(866\) −1.29071 23.8058i −0.0438602 0.808955i
\(867\) −6.15784 + 2.84892i −0.209131 + 0.0967545i
\(868\) −0.155578 0.0169202i −0.00528068 0.000574308i
\(869\) −14.1745 4.77594i −0.480837 0.162013i
\(870\) −0.192190 1.17230i −0.00651584 0.0397449i
\(871\) −4.52500 4.28630i −0.153324 0.145236i
\(872\) −1.13265 4.07943i −0.0383563 0.138147i
\(873\) −4.95990 9.35536i −0.167867 0.316631i
\(874\) 11.8802 4.00292i 0.401855 0.135401i
\(875\) −2.03090 + 0.447035i −0.0686570 + 0.0151126i
\(876\) 1.21443 4.37397i 0.0410317 0.147783i
\(877\) −40.9810 + 24.6575i −1.38383 + 0.832624i −0.996021 0.0891158i \(-0.971596\pi\)
−0.387810 + 0.921739i \(0.626768\pi\)
\(878\) −38.9890 + 4.24031i −1.31582 + 0.143104i
\(879\) −3.04214 0.669625i −0.102609 0.0225859i
\(880\) −0.194585 + 0.367026i −0.00655945 + 0.0123724i
\(881\) −2.15002 + 13.1145i −0.0724360 + 0.441840i 0.925562 + 0.378596i \(0.123593\pi\)
−0.997998 + 0.0632443i \(0.979855\pi\)
\(882\) 5.18461 3.94123i 0.174575 0.132708i
\(883\) 8.45845 + 9.95806i 0.284650 + 0.335115i 0.885840 0.463990i \(-0.153583\pi\)
−0.601191 + 0.799106i \(0.705307\pi\)
\(884\) −18.6110 −0.625956
\(885\) −1.37119 1.85742i −0.0460921 0.0624365i
\(886\) 21.3368 0.716823
\(887\) 34.2029 + 40.2667i 1.14842 + 1.35202i 0.926202 + 0.377028i \(0.123054\pi\)
0.222218 + 0.974997i \(0.428670\pi\)
\(888\) −3.51569 + 2.67256i −0.117979 + 0.0896852i
\(889\) −0.852937 + 5.20268i −0.0286066 + 0.174492i
\(890\) 0.461087 0.869703i 0.0154557 0.0291525i
\(891\) −1.34979 0.297110i −0.0452195 0.00995357i
\(892\) 3.09940 0.337080i 0.103776 0.0112863i
\(893\) 11.7312 7.05842i 0.392569 0.236201i
\(894\) 3.14096 11.3127i 0.105049 0.378354i
\(895\) 4.20816 0.926285i 0.140663 0.0309623i
\(896\) 0.661620 0.222926i 0.0221032 0.00744743i
\(897\) −6.05737 11.4254i −0.202250 0.381483i
\(898\) −3.41930 12.3152i −0.114103 0.410963i
\(899\) −0.643179 0.609252i −0.0214512 0.0203197i
\(900\) 0.794294 + 4.84498i 0.0264765 + 0.161499i
\(901\) 15.4973 + 5.22166i 0.516291 + 0.173959i
\(902\) −8.35558 0.908725i −0.278211 0.0302572i
\(903\) −0.917497 + 0.424479i −0.0305324 + 0.0141258i
\(904\) −0.830409 15.3160i −0.0276190 0.509403i
\(905\) −1.11614 0.848469i −0.0371018 0.0282041i
\(906\) 13.6193 12.9008i 0.452470 0.428602i
\(907\) 9.11419 + 5.48383i 0.302632 + 0.182087i 0.658767 0.752347i \(-0.271078\pi\)
−0.356135 + 0.934434i \(0.615906\pi\)
\(908\) 1.39206 + 0.644038i 0.0461973 + 0.0213731i
\(909\) −3.46816 + 8.70443i −0.115032 + 0.288708i
\(910\) 0.449398 + 0.662812i 0.0148974 + 0.0219720i
\(911\) 0.113977 0.168104i 0.00377624 0.00556954i −0.825796 0.563969i \(-0.809274\pi\)
0.829572 + 0.558399i \(0.188584\pi\)
\(912\) 1.36930 + 3.43668i 0.0453421 + 0.113800i
\(913\) −0.557685 + 10.2859i −0.0184567 + 0.340413i
\(914\) 10.6756 12.5682i 0.353116 0.415720i
\(915\) 0.313414 0.368980i 0.0103611 0.0121981i
\(916\) 0.894922 16.5059i 0.0295691 0.545369i
\(917\) 1.03081 + 2.58715i 0.0340405 + 0.0854352i
\(918\) 2.73690 4.03662i 0.0903311 0.133228i
\(919\) −3.98268 5.87401i −0.131376 0.193766i 0.756311 0.654212i \(-0.227000\pi\)
−0.887688 + 0.460446i \(0.847689\pi\)
\(920\) 0.377007 0.946217i 0.0124296 0.0311958i
\(921\) 4.74771 + 2.19653i 0.156442 + 0.0723780i
\(922\) −14.3469 8.63224i −0.472490 0.284288i
\(923\) 18.8081 17.8159i 0.619075 0.586419i
\(924\) 0.768179 + 0.583954i 0.0252712 + 0.0192107i
\(925\) 1.17384 + 21.6501i 0.0385955 + 0.711852i
\(926\) −14.1674 + 6.55455i −0.465570 + 0.215396i
\(927\) 16.0482 + 1.74534i 0.527091 + 0.0573246i
\(928\) 3.74545 + 1.26199i 0.122950 + 0.0414268i
\(929\) 6.61135 + 40.3275i 0.216911 + 1.32310i 0.840697 + 0.541506i \(0.182146\pi\)
−0.623786 + 0.781595i \(0.714406\pi\)
\(930\) −0.0489128 0.0463326i −0.00160391 0.00151931i
\(931\) −6.44550 23.2146i −0.211243 0.760827i
\(932\) −8.71230 16.4331i −0.285381 0.538286i
\(933\) −1.74740 + 0.588768i −0.0572074 + 0.0192754i
\(934\) −10.3673 + 2.28202i −0.339230 + 0.0746701i
\(935\) 0.542007 1.95213i 0.0177255 0.0638416i
\(936\) 3.26985 1.96740i 0.106878 0.0643065i
\(937\) 14.8435 1.61433i 0.484915 0.0527377i 0.137604 0.990487i \(-0.456060\pi\)
0.347312 + 0.937750i \(0.387095\pi\)
\(938\) −1.11366 0.245134i −0.0363621 0.00800391i
\(939\) 3.81508 7.19600i 0.124500 0.234832i
\(940\) 0.179959 1.09770i 0.00586962 0.0358031i
\(941\) −1.88415 + 1.43229i −0.0614214 + 0.0466913i −0.635434 0.772155i \(-0.719179\pi\)
0.574013 + 0.818846i \(0.305386\pi\)
\(942\) 6.37780 + 7.50852i 0.207800 + 0.244641i
\(943\) 20.6078 0.671083
\(944\) 7.59668 1.13595i 0.247251 0.0369721i
\(945\) −0.209848 −0.00682635
\(946\) 1.29558 + 1.52528i 0.0421230 + 0.0495911i
\(947\) −21.4685 + 16.3199i −0.697632 + 0.530326i −0.892805 0.450443i \(-0.851266\pi\)
0.195173 + 0.980769i \(0.437473\pi\)
\(948\) −1.75085 + 10.6797i −0.0568650 + 0.346861i
\(949\) −8.11420 + 15.3050i −0.263398 + 0.496821i
\(950\) 17.7383 + 3.90449i 0.575506 + 0.126679i
\(951\) 0.283885 0.0308743i 0.00920560 0.00100117i
\(952\) −2.91755 + 1.75543i −0.0945585 + 0.0568939i
\(953\) 0.613085 2.20813i 0.0198598 0.0715285i −0.952956 0.303108i \(-0.901976\pi\)
0.972816 + 0.231580i \(0.0743894\pi\)
\(954\) −3.27478 + 0.720834i −0.106025 + 0.0233379i
\(955\) −4.05191 + 1.36525i −0.131117 + 0.0441783i
\(956\) −12.4891 23.5569i −0.403925 0.761884i
\(957\) 1.46138 + 5.26342i 0.0472397 + 0.170142i
\(958\) −3.14193 2.97620i −0.101511 0.0961565i
\(959\) 0.657871 + 4.01283i 0.0212438 + 0.129581i
\(960\) 0.284836 + 0.0959723i 0.00919303 + 0.00309749i
\(961\) 30.7683 + 3.34626i 0.992527 + 0.107944i
\(962\) 15.2950 7.07620i 0.493129 0.228146i
\(963\) 0.568323 + 10.4821i 0.0183139 + 0.337781i
\(964\) −2.39689 1.82207i −0.0771986 0.0586848i
\(965\) 4.31197 4.08452i 0.138807 0.131485i
\(966\) −2.02726 1.21976i −0.0652259 0.0392451i
\(967\) 9.80152 + 4.53467i 0.315196 + 0.145825i 0.571108 0.820875i \(-0.306514\pi\)
−0.255912 + 0.966700i \(0.582376\pi\)
\(968\) −3.36448 + 8.44422i −0.108139 + 0.271407i
\(969\) −10.1250 14.9332i −0.325261 0.479724i
\(970\) −1.78608 + 2.63427i −0.0573475 + 0.0845813i
\(971\) 6.16932 + 15.4838i 0.197983 + 0.496900i 0.994129 0.108205i \(-0.0345104\pi\)
−0.796146 + 0.605105i \(0.793131\pi\)
\(972\) −0.0541389 + 0.998533i −0.00173651 + 0.0320280i
\(973\) −5.75782 + 6.77863i −0.184587 + 0.217313i
\(974\) −13.2884 + 15.6443i −0.425788 + 0.501276i
\(975\) 1.01433 18.7082i 0.0324846 0.599143i
\(976\) 0.596175 + 1.49629i 0.0190831 + 0.0478950i
\(977\) 12.2925 18.1300i 0.393271 0.580032i −0.578580 0.815625i \(-0.696393\pi\)
0.971852 + 0.235594i \(0.0757035\pi\)
\(978\) 1.95607 + 2.88499i 0.0625482 + 0.0922518i
\(979\) −1.67539 + 4.20491i −0.0535457 + 0.134390i
\(980\) −1.77656 0.821924i −0.0567501 0.0262554i
\(981\) −3.62772 2.18273i −0.115824 0.0696891i
\(982\) 10.4650 9.91296i 0.333951 0.316335i
\(983\) 3.59282 + 2.73119i 0.114593 + 0.0871114i 0.660901 0.750473i \(-0.270174\pi\)
−0.546308 + 0.837584i \(0.683967\pi\)
\(984\) 0.329231 + 6.07231i 0.0104955 + 0.193578i
\(985\) 0.497166 0.230013i 0.0158410 0.00732883i
\(986\) −19.1625 2.08405i −0.610259 0.0663696i
\(987\) −2.44854 0.825010i −0.0779380 0.0262604i
\(988\) −2.28394 13.9314i −0.0726617 0.443216i
\(989\) −3.56236 3.37444i −0.113276 0.107301i
\(990\) 0.111136 + 0.400275i 0.00353213 + 0.0127216i
\(991\) 13.7028 + 25.8462i 0.435283 + 0.821030i 0.999991 0.00426024i \(-0.00135608\pi\)
−0.564708 + 0.825291i \(0.691011\pi\)
\(992\) 0.212419 0.0715722i 0.00674430 0.00227242i
\(993\) 27.7818 6.11524i 0.881629 0.194061i
\(994\) 1.26800 4.56694i 0.0402186 0.144854i
\(995\) −1.54062 + 0.926961i −0.0488410 + 0.0293867i
\(996\) 7.40947 0.805829i 0.234778 0.0255337i
\(997\) 50.4003 + 11.0939i 1.59619 + 0.351349i 0.921995 0.387202i \(-0.126558\pi\)
0.674198 + 0.738551i \(0.264489\pi\)
\(998\) −13.2193 + 24.9343i −0.418450 + 0.789280i
\(999\) −0.714458 + 4.35800i −0.0226045 + 0.137881i
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 354.2.e.b.223.2 yes 56
59.9 even 29 inner 354.2.e.b.127.2 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.2.e.b.127.2 56 59.9 even 29 inner
354.2.e.b.223.2 yes 56 1.1 even 1 trivial