Properties

Label 560.2.bb.c.29.2
Level $560$
Weight $2$
Character 560.29
Analytic conductor $4.472$
Analytic rank $0$
Dimension $70$
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] = [560,2,Mod(29,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bb (of order \(4\), degree \(2\), 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: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 29.2
Character \(\chi\) \(=\) 560.29
Dual form 560.2.bb.c.309.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40637 - 0.148759i) q^{2} +(-0.279102 + 0.279102i) q^{3} +(1.95574 + 0.418421i) q^{4} +(2.19030 - 0.450071i) q^{5} +(0.434038 - 0.351001i) q^{6} -1.00000 q^{7} +(-2.68825 - 0.879388i) q^{8} +2.84420i q^{9} +O(q^{10})\) \(q+(-1.40637 - 0.148759i) q^{2} +(-0.279102 + 0.279102i) q^{3} +(1.95574 + 0.418421i) q^{4} +(2.19030 - 0.450071i) q^{5} +(0.434038 - 0.351001i) q^{6} -1.00000 q^{7} +(-2.68825 - 0.879388i) q^{8} +2.84420i q^{9} +(-3.14733 + 0.307138i) q^{10} +(-2.35311 + 2.35311i) q^{11} +(-0.662632 + 0.429069i) q^{12} +(-2.34702 + 2.34702i) q^{13} +(1.40637 + 0.148759i) q^{14} +(-0.485702 + 0.736933i) q^{15} +(3.64985 + 1.63664i) q^{16} +3.39463i q^{17} +(0.423102 - 4.00000i) q^{18} +(-0.847544 - 0.847544i) q^{19} +(4.47199 + 0.0362455i) q^{20} +(0.279102 - 0.279102i) q^{21} +(3.65939 - 2.95929i) q^{22} -2.16644 q^{23} +(0.995733 - 0.504856i) q^{24} +(4.59487 - 1.97159i) q^{25} +(3.64992 - 2.95163i) q^{26} +(-1.63113 - 1.63113i) q^{27} +(-1.95574 - 0.418421i) q^{28} +(-2.00809 - 2.00809i) q^{29} +(0.792701 - 0.964147i) q^{30} -2.92187 q^{31} +(-4.88956 - 2.84467i) q^{32} -1.31351i q^{33} +(0.504982 - 4.77410i) q^{34} +(-2.19030 + 0.450071i) q^{35} +(-1.19007 + 5.56253i) q^{36} +(5.03883 + 5.03883i) q^{37} +(1.06588 + 1.31804i) q^{38} -1.31011i q^{39} +(-6.28387 - 0.716224i) q^{40} +11.0535i q^{41} +(-0.434038 + 0.351001i) q^{42} +(4.96192 + 4.96192i) q^{43} +(-5.58667 + 3.61749i) q^{44} +(1.28009 + 6.22968i) q^{45} +(3.04682 + 0.322278i) q^{46} -7.39580i q^{47} +(-1.47547 + 0.561888i) q^{48} +1.00000 q^{49} +(-6.75537 + 2.08925i) q^{50} +(-0.947446 - 0.947446i) q^{51} +(-5.57221 + 3.60813i) q^{52} +(-1.62915 - 1.62915i) q^{53} +(2.05132 + 2.53661i) q^{54} +(-4.09496 + 6.21310i) q^{55} +(2.68825 + 0.879388i) q^{56} +0.473102 q^{57} +(2.52539 + 3.12284i) q^{58} +(-5.55555 + 5.55555i) q^{59} +(-1.25826 + 1.23802i) q^{60} +(0.540392 + 0.540392i) q^{61} +(4.10923 + 0.434656i) q^{62} -2.84420i q^{63} +(6.45335 + 4.72803i) q^{64} +(-4.08437 + 6.19702i) q^{65} +(-0.195397 + 1.84728i) q^{66} +(4.69437 - 4.69437i) q^{67} +(-1.42038 + 6.63901i) q^{68} +(0.604658 - 0.604658i) q^{69} +(3.14733 - 0.307138i) q^{70} +16.1009i q^{71} +(2.50116 - 7.64593i) q^{72} +5.31323 q^{73} +(-6.33688 - 7.83603i) q^{74} +(-0.732163 + 1.83271i) q^{75} +(-1.30295 - 2.01221i) q^{76} +(2.35311 - 2.35311i) q^{77} +(-0.194892 + 1.84250i) q^{78} +3.05814 q^{79} +(8.73089 + 1.94206i) q^{80} -7.62211 q^{81} +(1.64432 - 15.5453i) q^{82} +(-5.46375 + 5.46375i) q^{83} +(0.662632 - 0.429069i) q^{84} +(1.52782 + 7.43527i) q^{85} +(-6.24015 - 7.71642i) q^{86} +1.12092 q^{87} +(8.39504 - 4.25645i) q^{88} -16.8612i q^{89} +(-0.873562 - 8.95164i) q^{90} +(2.34702 - 2.34702i) q^{91} +(-4.23700 - 0.906484i) q^{92} +(0.815499 - 0.815499i) q^{93} +(-1.10019 + 10.4012i) q^{94} +(-2.23783 - 1.47492i) q^{95} +(2.15864 - 0.570732i) q^{96} +6.16712i q^{97} +(-1.40637 - 0.148759i) q^{98} +(-6.69273 - 6.69273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} + 18 q^{18} + 14 q^{19} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 q^{50} + 8 q^{51} - 28 q^{52} + 30 q^{53} - 32 q^{54} - 6 q^{55} + 8 q^{56} + 76 q^{57} - 56 q^{58} + 2 q^{59} - 64 q^{60} + 30 q^{61} - 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} - 6 q^{67} + 36 q^{68} - 16 q^{69} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 q^{80} - 82 q^{81} - 24 q^{82} - 10 q^{83} - 4 q^{84} - 32 q^{85} + 32 q^{86} + 4 q^{87} - 32 q^{88} + 158 q^{90} + 6 q^{91} + 92 q^{92} + 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} - 2 q^{98} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40637 0.148759i −0.994452 0.105189i
\(3\) −0.279102 + 0.279102i −0.161139 + 0.161139i −0.783071 0.621932i \(-0.786348\pi\)
0.621932 + 0.783071i \(0.286348\pi\)
\(4\) 1.95574 + 0.418421i 0.977871 + 0.209210i
\(5\) 2.19030 0.450071i 0.979534 0.201278i
\(6\) 0.434038 0.351001i 0.177195 0.143295i
\(7\) −1.00000 −0.377964
\(8\) −2.68825 0.879388i −0.950439 0.310911i
\(9\) 2.84420i 0.948068i
\(10\) −3.14733 + 0.307138i −0.995272 + 0.0971254i
\(11\) −2.35311 + 2.35311i −0.709490 + 0.709490i −0.966428 0.256938i \(-0.917286\pi\)
0.256938 + 0.966428i \(0.417286\pi\)
\(12\) −0.662632 + 0.429069i −0.191285 + 0.123861i
\(13\) −2.34702 + 2.34702i −0.650947 + 0.650947i −0.953221 0.302274i \(-0.902254\pi\)
0.302274 + 0.953221i \(0.402254\pi\)
\(14\) 1.40637 + 0.148759i 0.375868 + 0.0397576i
\(15\) −0.485702 + 0.736933i −0.125408 + 0.190275i
\(16\) 3.64985 + 1.63664i 0.912462 + 0.409161i
\(17\) 3.39463i 0.823318i 0.911338 + 0.411659i \(0.135051\pi\)
−0.911338 + 0.411659i \(0.864949\pi\)
\(18\) 0.423102 4.00000i 0.0997261 0.942809i
\(19\) −0.847544 0.847544i −0.194440 0.194440i 0.603172 0.797611i \(-0.293903\pi\)
−0.797611 + 0.603172i \(0.793903\pi\)
\(20\) 4.47199 + 0.0362455i 0.999967 + 0.00810475i
\(21\) 0.279102 0.279102i 0.0609050 0.0609050i
\(22\) 3.65939 2.95929i 0.780184 0.630923i
\(23\) −2.16644 −0.451734 −0.225867 0.974158i \(-0.572522\pi\)
−0.225867 + 0.974158i \(0.572522\pi\)
\(24\) 0.995733 0.504856i 0.203253 0.103053i
\(25\) 4.59487 1.97159i 0.918974 0.394317i
\(26\) 3.64992 2.95163i 0.715808 0.578863i
\(27\) −1.63113 1.63113i −0.313910 0.313910i
\(28\) −1.95574 0.418421i −0.369600 0.0790740i
\(29\) −2.00809 2.00809i −0.372893 0.372893i 0.495637 0.868530i \(-0.334935\pi\)
−0.868530 + 0.495637i \(0.834935\pi\)
\(30\) 0.792701 0.964147i 0.144727 0.176028i
\(31\) −2.92187 −0.524784 −0.262392 0.964961i \(-0.584511\pi\)
−0.262392 + 0.964961i \(0.584511\pi\)
\(32\) −4.88956 2.84467i −0.864361 0.502872i
\(33\) 1.31351i 0.228653i
\(34\) 0.504982 4.77410i 0.0866038 0.818751i
\(35\) −2.19030 + 0.450071i −0.370229 + 0.0760759i
\(36\) −1.19007 + 5.56253i −0.198346 + 0.927088i
\(37\) 5.03883 + 5.03883i 0.828379 + 0.828379i 0.987293 0.158913i \(-0.0507991\pi\)
−0.158913 + 0.987293i \(0.550799\pi\)
\(38\) 1.06588 + 1.31804i 0.172908 + 0.213814i
\(39\) 1.31011i 0.209786i
\(40\) −6.28387 0.716224i −0.993567 0.113245i
\(41\) 11.0535i 1.72627i 0.504971 + 0.863136i \(0.331503\pi\)
−0.504971 + 0.863136i \(0.668497\pi\)
\(42\) −0.434038 + 0.351001i −0.0669736 + 0.0541606i
\(43\) 4.96192 + 4.96192i 0.756686 + 0.756686i 0.975718 0.219032i \(-0.0702899\pi\)
−0.219032 + 0.975718i \(0.570290\pi\)
\(44\) −5.58667 + 3.61749i −0.842222 + 0.545357i
\(45\) 1.28009 + 6.22968i 0.190825 + 0.928665i
\(46\) 3.04682 + 0.322278i 0.449228 + 0.0475174i
\(47\) 7.39580i 1.07879i −0.842053 0.539394i \(-0.818653\pi\)
0.842053 0.539394i \(-0.181347\pi\)
\(48\) −1.47547 + 0.561888i −0.212966 + 0.0811016i
\(49\) 1.00000 0.142857
\(50\) −6.75537 + 2.08925i −0.955354 + 0.295464i
\(51\) −0.947446 0.947446i −0.132669 0.132669i
\(52\) −5.57221 + 3.60813i −0.772726 + 0.500357i
\(53\) −1.62915 1.62915i −0.223781 0.223781i 0.586307 0.810089i \(-0.300581\pi\)
−0.810089 + 0.586307i \(0.800581\pi\)
\(54\) 2.05132 + 2.53661i 0.279149 + 0.345189i
\(55\) −4.09496 + 6.21310i −0.552165 + 0.837774i
\(56\) 2.68825 + 0.879388i 0.359232 + 0.117513i
\(57\) 0.473102 0.0626639
\(58\) 2.52539 + 3.12284i 0.331601 + 0.410049i
\(59\) −5.55555 + 5.55555i −0.723271 + 0.723271i −0.969270 0.245999i \(-0.920884\pi\)
0.245999 + 0.969270i \(0.420884\pi\)
\(60\) −1.25826 + 1.23802i −0.162440 + 0.159828i
\(61\) 0.540392 + 0.540392i 0.0691901 + 0.0691901i 0.740855 0.671665i \(-0.234421\pi\)
−0.671665 + 0.740855i \(0.734421\pi\)
\(62\) 4.10923 + 0.434656i 0.521873 + 0.0552013i
\(63\) 2.84420i 0.358336i
\(64\) 6.45335 + 4.72803i 0.806669 + 0.591003i
\(65\) −4.08437 + 6.19702i −0.506603 + 0.768646i
\(66\) −0.195397 + 1.84728i −0.0240518 + 0.227385i
\(67\) 4.69437 4.69437i 0.573508 0.573508i −0.359599 0.933107i \(-0.617086\pi\)
0.933107 + 0.359599i \(0.117086\pi\)
\(68\) −1.42038 + 6.63901i −0.172247 + 0.805099i
\(69\) 0.604658 0.604658i 0.0727922 0.0727922i
\(70\) 3.14733 0.307138i 0.376178 0.0367100i
\(71\) 16.1009i 1.91082i 0.295276 + 0.955412i \(0.404589\pi\)
−0.295276 + 0.955412i \(0.595411\pi\)
\(72\) 2.50116 7.64593i 0.294764 0.901081i
\(73\) 5.31323 0.621866 0.310933 0.950432i \(-0.399359\pi\)
0.310933 + 0.950432i \(0.399359\pi\)
\(74\) −6.33688 7.83603i −0.736647 0.910920i
\(75\) −0.732163 + 1.83271i −0.0845429 + 0.211623i
\(76\) −1.30295 2.01221i −0.149458 0.230816i
\(77\) 2.35311 2.35311i 0.268162 0.268162i
\(78\) −0.194892 + 1.84250i −0.0220671 + 0.208622i
\(79\) 3.05814 0.344068 0.172034 0.985091i \(-0.444966\pi\)
0.172034 + 0.985091i \(0.444966\pi\)
\(80\) 8.73089 + 1.94206i 0.976143 + 0.217129i
\(81\) −7.62211 −0.846902
\(82\) 1.64432 15.5453i 0.181584 1.71670i
\(83\) −5.46375 + 5.46375i −0.599725 + 0.599725i −0.940239 0.340515i \(-0.889399\pi\)
0.340515 + 0.940239i \(0.389399\pi\)
\(84\) 0.662632 0.429069i 0.0722991 0.0468152i
\(85\) 1.52782 + 7.43527i 0.165716 + 0.806468i
\(86\) −6.24015 7.71642i −0.672893 0.832083i
\(87\) 1.12092 0.120176
\(88\) 8.39504 4.25645i 0.894915 0.453739i
\(89\) 16.8612i 1.78728i −0.448780 0.893642i \(-0.648141\pi\)
0.448780 0.893642i \(-0.351859\pi\)
\(90\) −0.873562 8.95164i −0.0920815 0.943586i
\(91\) 2.34702 2.34702i 0.246035 0.246035i
\(92\) −4.23700 0.906484i −0.441738 0.0945075i
\(93\) 0.815499 0.815499i 0.0845634 0.0845634i
\(94\) −1.10019 + 10.4012i −0.113476 + 1.07280i
\(95\) −2.23783 1.47492i −0.229597 0.151324i
\(96\) 2.15864 0.570732i 0.220315 0.0582501i
\(97\) 6.16712i 0.626176i 0.949724 + 0.313088i \(0.101363\pi\)
−0.949724 + 0.313088i \(0.898637\pi\)
\(98\) −1.40637 0.148759i −0.142065 0.0150270i
\(99\) −6.69273 6.69273i −0.672645 0.672645i
\(100\) 9.81133 1.93333i 0.981133 0.193333i
\(101\) 6.08324 6.08324i 0.605305 0.605305i −0.336410 0.941716i \(-0.609213\pi\)
0.941716 + 0.336410i \(0.109213\pi\)
\(102\) 1.19152 + 1.47340i 0.117978 + 0.145888i
\(103\) 16.0661 1.58304 0.791519 0.611145i \(-0.209291\pi\)
0.791519 + 0.611145i \(0.209291\pi\)
\(104\) 8.37332 4.24543i 0.821071 0.416299i
\(105\) 0.485702 0.736933i 0.0473997 0.0719173i
\(106\) 2.04883 + 2.53354i 0.199000 + 0.246079i
\(107\) −12.1468 12.1468i −1.17428 1.17428i −0.981180 0.193097i \(-0.938147\pi\)
−0.193097 0.981180i \(-0.561853\pi\)
\(108\) −2.50757 3.87256i −0.241291 0.372637i
\(109\) −4.17642 4.17642i −0.400029 0.400029i 0.478215 0.878243i \(-0.341284\pi\)
−0.878243 + 0.478215i \(0.841284\pi\)
\(110\) 6.68328 8.12874i 0.637226 0.775045i
\(111\) −2.81269 −0.266969
\(112\) −3.64985 1.63664i −0.344878 0.154648i
\(113\) 14.0838i 1.32489i 0.749111 + 0.662444i \(0.230481\pi\)
−0.749111 + 0.662444i \(0.769519\pi\)
\(114\) −0.665355 0.0703783i −0.0623162 0.00659153i
\(115\) −4.74517 + 0.975054i −0.442489 + 0.0909242i
\(116\) −3.08708 4.76754i −0.286628 0.442655i
\(117\) −6.67541 6.67541i −0.617142 0.617142i
\(118\) 8.63958 6.98670i 0.795338 0.643178i
\(119\) 3.39463i 0.311185i
\(120\) 1.95374 1.55394i 0.178351 0.141855i
\(121\) 0.0742641i 0.00675128i
\(122\) −0.679602 0.840378i −0.0615283 0.0760843i
\(123\) −3.08506 3.08506i −0.278171 0.278171i
\(124\) −5.71443 1.22257i −0.513171 0.109790i
\(125\) 9.17682 6.38640i 0.820799 0.571217i
\(126\) −0.423102 + 4.00000i −0.0376929 + 0.356348i
\(127\) 0.331675i 0.0294314i 0.999892 + 0.0147157i \(0.00468432\pi\)
−0.999892 + 0.0147157i \(0.995316\pi\)
\(128\) −8.37245 7.60934i −0.740027 0.672577i
\(129\) −2.76976 −0.243864
\(130\) 6.66599 8.10770i 0.584646 0.711093i
\(131\) −4.88335 4.88335i −0.426660 0.426660i 0.460829 0.887489i \(-0.347552\pi\)
−0.887489 + 0.460829i \(0.847552\pi\)
\(132\) 0.549601 2.56889i 0.0478366 0.223594i
\(133\) 0.847544 + 0.847544i 0.0734914 + 0.0734914i
\(134\) −7.30034 + 5.90367i −0.630653 + 0.510000i
\(135\) −4.30679 2.83854i −0.370669 0.244303i
\(136\) 2.98519 9.12560i 0.255978 0.782514i
\(137\) 10.8530 0.927237 0.463619 0.886035i \(-0.346551\pi\)
0.463619 + 0.886035i \(0.346551\pi\)
\(138\) −0.940319 + 0.760423i −0.0800453 + 0.0647315i
\(139\) 11.5768 11.5768i 0.981935 0.981935i −0.0179046 0.999840i \(-0.505700\pi\)
0.999840 + 0.0179046i \(0.00569953\pi\)
\(140\) −4.47199 0.0362455i −0.377952 0.00306331i
\(141\) 2.06418 + 2.06418i 0.173835 + 0.173835i
\(142\) 2.39516 22.6438i 0.200997 1.90022i
\(143\) 11.0456i 0.923680i
\(144\) −4.65495 + 10.3809i −0.387913 + 0.865076i
\(145\) −5.30212 3.49455i −0.440317 0.290207i
\(146\) −7.47235 0.790392i −0.618416 0.0654133i
\(147\) −0.279102 + 0.279102i −0.0230199 + 0.0230199i
\(148\) 7.74630 + 11.9630i 0.636742 + 0.983353i
\(149\) 9.32319 9.32319i 0.763785 0.763785i −0.213219 0.977004i \(-0.568395\pi\)
0.977004 + 0.213219i \(0.0683948\pi\)
\(150\) 1.30232 2.46855i 0.106334 0.201556i
\(151\) 18.4845i 1.50425i 0.659023 + 0.752123i \(0.270970\pi\)
−0.659023 + 0.752123i \(0.729030\pi\)
\(152\) 1.53309 + 3.02373i 0.124350 + 0.245257i
\(153\) −9.65502 −0.780562
\(154\) −3.65939 + 2.95929i −0.294882 + 0.238467i
\(155\) −6.39979 + 1.31505i −0.514044 + 0.105627i
\(156\) 0.548179 2.56225i 0.0438894 0.205144i
\(157\) 13.3909 13.3909i 1.06871 1.06871i 0.0712495 0.997459i \(-0.477301\pi\)
0.997459 0.0712495i \(-0.0226987\pi\)
\(158\) −4.30088 0.454927i −0.342159 0.0361921i
\(159\) 0.909397 0.0721199
\(160\) −11.9899 4.03005i −0.947888 0.318603i
\(161\) 2.16644 0.170740
\(162\) 10.7195 + 1.13386i 0.842203 + 0.0890845i
\(163\) −3.01843 + 3.01843i −0.236421 + 0.236421i −0.815366 0.578945i \(-0.803465\pi\)
0.578945 + 0.815366i \(0.303465\pi\)
\(164\) −4.62503 + 21.6179i −0.361154 + 1.68807i
\(165\) −0.591175 2.87700i −0.0460229 0.223974i
\(166\) 8.49683 6.87126i 0.659482 0.533313i
\(167\) −4.35664 −0.337127 −0.168563 0.985691i \(-0.553913\pi\)
−0.168563 + 0.985691i \(0.553913\pi\)
\(168\) −0.995733 + 0.504856i −0.0768225 + 0.0389505i
\(169\) 1.98298i 0.152537i
\(170\) −1.04262 10.6840i −0.0799651 0.819426i
\(171\) 2.41059 2.41059i 0.184342 0.184342i
\(172\) 7.62806 + 11.7804i 0.581634 + 0.898247i
\(173\) −4.72170 + 4.72170i −0.358984 + 0.358984i −0.863439 0.504454i \(-0.831694\pi\)
0.504454 + 0.863439i \(0.331694\pi\)
\(174\) −1.57643 0.166748i −0.119509 0.0126411i
\(175\) −4.59487 + 1.97159i −0.347340 + 0.149038i
\(176\) −12.4397 + 4.73729i −0.937678 + 0.357087i
\(177\) 3.10112i 0.233095i
\(178\) −2.50826 + 23.7131i −0.188002 + 1.77737i
\(179\) −1.50187 1.50187i −0.112255 0.112255i 0.648748 0.761003i \(-0.275293\pi\)
−0.761003 + 0.648748i \(0.775293\pi\)
\(180\) −0.103090 + 12.7193i −0.00768385 + 0.948037i
\(181\) 15.6686 15.6686i 1.16463 1.16463i 0.181185 0.983449i \(-0.442007\pi\)
0.983449 0.181185i \(-0.0579933\pi\)
\(182\) −3.64992 + 2.95163i −0.270550 + 0.218790i
\(183\) −0.301649 −0.0222985
\(184\) 5.82393 + 1.90514i 0.429346 + 0.140449i
\(185\) 13.3044 + 8.76875i 0.978160 + 0.644691i
\(186\) −1.26821 + 1.02558i −0.0929893 + 0.0751991i
\(187\) −7.98794 7.98794i −0.584136 0.584136i
\(188\) 3.09456 14.4643i 0.225694 1.05492i
\(189\) 1.63113 + 1.63113i 0.118647 + 0.118647i
\(190\) 2.92781 + 2.40719i 0.212406 + 0.174636i
\(191\) 23.1607 1.67585 0.837925 0.545786i \(-0.183769\pi\)
0.837925 + 0.545786i \(0.183769\pi\)
\(192\) −3.12074 + 0.481542i −0.225220 + 0.0347523i
\(193\) 9.42975i 0.678768i 0.940648 + 0.339384i \(0.110219\pi\)
−0.940648 + 0.339384i \(0.889781\pi\)
\(194\) 0.917416 8.67323i 0.0658666 0.622702i
\(195\) −0.589645 2.86955i −0.0422254 0.205493i
\(196\) 1.95574 + 0.418421i 0.139696 + 0.0298872i
\(197\) −12.9007 12.9007i −0.919137 0.919137i 0.0778293 0.996967i \(-0.475201\pi\)
−0.996967 + 0.0778293i \(0.975201\pi\)
\(198\) 8.41683 + 10.4080i 0.598158 + 0.739668i
\(199\) 5.19391i 0.368186i −0.982909 0.184093i \(-0.941065\pi\)
0.982909 0.184093i \(-0.0589348\pi\)
\(200\) −14.0859 + 1.25944i −0.996027 + 0.0890558i
\(201\) 2.62041i 0.184829i
\(202\) −9.46022 + 7.65034i −0.665619 + 0.538276i
\(203\) 2.00809 + 2.00809i 0.140940 + 0.140940i
\(204\) −1.45653 2.24939i −0.101977 0.157489i
\(205\) 4.97488 + 24.2106i 0.347461 + 1.69094i
\(206\) −22.5948 2.38998i −1.57425 0.166518i
\(207\) 6.16181i 0.428275i
\(208\) −12.4075 + 4.72503i −0.860306 + 0.327622i
\(209\) 3.98873 0.275906
\(210\) −0.792701 + 0.964147i −0.0547016 + 0.0665324i
\(211\) −11.1488 11.1488i −0.767518 0.767518i 0.210151 0.977669i \(-0.432604\pi\)
−0.977669 + 0.210151i \(0.932604\pi\)
\(212\) −2.50453 3.86787i −0.172012 0.265646i
\(213\) −4.49378 4.49378i −0.307909 0.307909i
\(214\) 15.2759 + 18.8898i 1.04424 + 1.29128i
\(215\) 13.1013 + 8.63490i 0.893504 + 0.588895i
\(216\) 2.95048 + 5.81927i 0.200755 + 0.395951i
\(217\) 2.92187 0.198350
\(218\) 5.25230 + 6.49486i 0.355731 + 0.439888i
\(219\) −1.48293 + 1.48293i −0.100207 + 0.100207i
\(220\) −10.6084 + 10.4378i −0.715217 + 0.703716i
\(221\) −7.96726 7.96726i −0.535936 0.535936i
\(222\) 3.95568 + 0.418414i 0.265488 + 0.0280821i
\(223\) 8.80142i 0.589387i 0.955592 + 0.294693i \(0.0952175\pi\)
−0.955592 + 0.294693i \(0.904782\pi\)
\(224\) 4.88956 + 2.84467i 0.326698 + 0.190068i
\(225\) 5.60760 + 13.0688i 0.373840 + 0.871250i
\(226\) 2.09509 19.8069i 0.139363 1.31754i
\(227\) −0.588561 + 0.588561i −0.0390642 + 0.0390642i −0.726369 0.687305i \(-0.758794\pi\)
0.687305 + 0.726369i \(0.258794\pi\)
\(228\) 0.925265 + 0.197955i 0.0612771 + 0.0131099i
\(229\) 17.3161 17.3161i 1.14428 1.14428i 0.156625 0.987658i \(-0.449939\pi\)
0.987658 0.156625i \(-0.0500615\pi\)
\(230\) 6.81850 0.665396i 0.449599 0.0438749i
\(231\) 1.31351i 0.0864229i
\(232\) 3.63236 + 7.16414i 0.238476 + 0.470349i
\(233\) −17.7261 −1.16128 −0.580639 0.814161i \(-0.697197\pi\)
−0.580639 + 0.814161i \(0.697197\pi\)
\(234\) 8.39505 + 10.3811i 0.548802 + 0.678634i
\(235\) −3.32864 16.1991i −0.217136 1.05671i
\(236\) −13.1898 + 8.54066i −0.858581 + 0.555949i
\(237\) −0.853533 + 0.853533i −0.0554429 + 0.0554429i
\(238\) −0.504982 + 4.77410i −0.0327331 + 0.309459i
\(239\) −8.20370 −0.530653 −0.265327 0.964159i \(-0.585480\pi\)
−0.265327 + 0.964159i \(0.585480\pi\)
\(240\) −2.97884 + 1.89477i −0.192283 + 0.122307i
\(241\) −18.5239 −1.19323 −0.596614 0.802529i \(-0.703488\pi\)
−0.596614 + 0.802529i \(0.703488\pi\)
\(242\) −0.0110475 + 0.104443i −0.000710158 + 0.00671383i
\(243\) 7.02072 7.02072i 0.450380 0.450380i
\(244\) 0.830756 + 1.28298i 0.0531837 + 0.0821343i
\(245\) 2.19030 0.450071i 0.139933 0.0287540i
\(246\) 3.87980 + 4.79766i 0.247367 + 0.305888i
\(247\) 3.97841 0.253140
\(248\) 7.85472 + 2.56946i 0.498775 + 0.163161i
\(249\) 3.04988i 0.193278i
\(250\) −13.8560 + 7.61649i −0.876331 + 0.481709i
\(251\) −2.93641 + 2.93641i −0.185345 + 0.185345i −0.793680 0.608335i \(-0.791838\pi\)
0.608335 + 0.793680i \(0.291838\pi\)
\(252\) 1.19007 5.56253i 0.0749676 0.350406i
\(253\) 5.09788 5.09788i 0.320501 0.320501i
\(254\) 0.0493397 0.466457i 0.00309585 0.0292681i
\(255\) −2.50161 1.64878i −0.156657 0.103250i
\(256\) 10.6428 + 11.9470i 0.665174 + 0.746688i
\(257\) 1.51474i 0.0944868i −0.998883 0.0472434i \(-0.984956\pi\)
0.998883 0.0472434i \(-0.0150436\pi\)
\(258\) 3.89530 + 0.412027i 0.242511 + 0.0256517i
\(259\) −5.03883 5.03883i −0.313098 0.313098i
\(260\) −10.5809 + 10.4108i −0.656201 + 0.645649i
\(261\) 5.71143 5.71143i 0.353528 0.353528i
\(262\) 6.14134 + 7.59423i 0.379413 + 0.469173i
\(263\) 16.5420 1.02003 0.510013 0.860167i \(-0.329641\pi\)
0.510013 + 0.860167i \(0.329641\pi\)
\(264\) −1.15509 + 3.53105i −0.0710908 + 0.217321i
\(265\) −4.30157 2.83510i −0.264243 0.174159i
\(266\) −1.06588 1.31804i −0.0653532 0.0808141i
\(267\) 4.70599 + 4.70599i 0.288002 + 0.288002i
\(268\) 11.1452 7.21675i 0.680800 0.440833i
\(269\) 7.26394 + 7.26394i 0.442890 + 0.442890i 0.892982 0.450092i \(-0.148609\pi\)
−0.450092 + 0.892982i \(0.648609\pi\)
\(270\) 5.63467 + 4.63271i 0.342915 + 0.281938i
\(271\) 10.4016 0.631853 0.315927 0.948784i \(-0.397685\pi\)
0.315927 + 0.948784i \(0.397685\pi\)
\(272\) −5.55580 + 12.3899i −0.336870 + 0.751247i
\(273\) 1.31011i 0.0792918i
\(274\) −15.2634 1.61449i −0.922093 0.0975349i
\(275\) −6.17288 + 15.4516i −0.372239 + 0.931767i
\(276\) 1.43555 0.929553i 0.0864103 0.0559525i
\(277\) −3.02860 3.02860i −0.181971 0.181971i 0.610243 0.792214i \(-0.291072\pi\)
−0.792214 + 0.610243i \(0.791072\pi\)
\(278\) −18.0035 + 14.5591i −1.07978 + 0.873199i
\(279\) 8.31041i 0.497531i
\(280\) 6.28387 + 0.716224i 0.375533 + 0.0428026i
\(281\) 26.6477i 1.58967i 0.606827 + 0.794834i \(0.292442\pi\)
−0.606827 + 0.794834i \(0.707558\pi\)
\(282\) −2.59593 3.21006i −0.154585 0.191156i
\(283\) −1.79947 1.79947i −0.106967 0.106967i 0.651598 0.758565i \(-0.274099\pi\)
−0.758565 + 0.651598i \(0.774099\pi\)
\(284\) −6.73694 + 31.4892i −0.399764 + 1.86854i
\(285\) 1.03624 0.212930i 0.0613814 0.0126129i
\(286\) −1.64314 + 15.5342i −0.0971607 + 0.918556i
\(287\) 11.0535i 0.652470i
\(288\) 8.09083 13.9069i 0.476757 0.819473i
\(289\) 5.47650 0.322147
\(290\) 6.93689 + 5.70336i 0.407348 + 0.334913i
\(291\) −1.72125 1.72125i −0.100902 0.100902i
\(292\) 10.3913 + 2.22316i 0.608105 + 0.130101i
\(293\) −2.16307 2.16307i −0.126368 0.126368i 0.641094 0.767462i \(-0.278481\pi\)
−0.767462 + 0.641094i \(0.778481\pi\)
\(294\) 0.434038 0.351001i 0.0253136 0.0204708i
\(295\) −9.66795 + 14.6687i −0.562890 + 0.854047i
\(296\) −9.11454 17.9767i −0.529772 1.04488i
\(297\) 7.67645 0.445433
\(298\) −14.4987 + 11.7249i −0.839890 + 0.679206i
\(299\) 5.08469 5.08469i 0.294055 0.294055i
\(300\) −2.19876 + 3.27795i −0.126946 + 0.189253i
\(301\) −4.96192 4.96192i −0.286000 0.286000i
\(302\) 2.74974 25.9960i 0.158230 1.49590i
\(303\) 3.39569i 0.195077i
\(304\) −1.70628 4.48054i −0.0978618 0.256976i
\(305\) 1.42684 + 0.940409i 0.0817005 + 0.0538476i
\(306\) 13.5785 + 1.43627i 0.776231 + 0.0821063i
\(307\) −17.9609 + 17.9609i −1.02508 + 1.02508i −0.0254033 + 0.999677i \(0.508087\pi\)
−0.999677 + 0.0254033i \(0.991913\pi\)
\(308\) 5.58667 3.61749i 0.318330 0.206125i
\(309\) −4.48407 + 4.48407i −0.255090 + 0.255090i
\(310\) 9.19609 0.897417i 0.522303 0.0509699i
\(311\) 17.0625i 0.967527i −0.875199 0.483764i \(-0.839269\pi\)
0.875199 0.483764i \(-0.160731\pi\)
\(312\) −1.15210 + 3.52191i −0.0652248 + 0.199389i
\(313\) −12.1923 −0.689147 −0.344574 0.938759i \(-0.611976\pi\)
−0.344574 + 0.938759i \(0.611976\pi\)
\(314\) −20.8245 + 16.8405i −1.17520 + 0.950363i
\(315\) −1.28009 6.22968i −0.0721252 0.351002i
\(316\) 5.98094 + 1.27959i 0.336454 + 0.0719826i
\(317\) −13.2752 + 13.2752i −0.745611 + 0.745611i −0.973652 0.228040i \(-0.926768\pi\)
0.228040 + 0.973652i \(0.426768\pi\)
\(318\) −1.27895 0.135281i −0.0717198 0.00758620i
\(319\) 9.45053 0.529128
\(320\) 16.2628 + 7.45135i 0.909116 + 0.416543i
\(321\) 6.78039 0.378444
\(322\) −3.04682 0.322278i −0.169792 0.0179599i
\(323\) 2.87710 2.87710i 0.160086 0.160086i
\(324\) −14.9069 3.18925i −0.828160 0.177180i
\(325\) −6.15691 + 15.4116i −0.341524 + 0.854883i
\(326\) 4.69404 3.79600i 0.259979 0.210241i
\(327\) 2.33129 0.128921
\(328\) 9.72035 29.7147i 0.536716 1.64072i
\(329\) 7.39580i 0.407744i
\(330\) 0.403430 + 4.13406i 0.0222081 + 0.227572i
\(331\) −10.9561 + 10.9561i −0.602199 + 0.602199i −0.940896 0.338697i \(-0.890014\pi\)
0.338697 + 0.940896i \(0.390014\pi\)
\(332\) −12.9718 + 8.39954i −0.711922 + 0.460985i
\(333\) −14.3315 + 14.3315i −0.785360 + 0.785360i
\(334\) 6.12704 + 0.648090i 0.335257 + 0.0354619i
\(335\) 8.16929 12.3949i 0.446336 0.677205i
\(336\) 1.47547 0.561888i 0.0804934 0.0306535i
\(337\) 0.474560i 0.0258509i 0.999916 + 0.0129255i \(0.00411441\pi\)
−0.999916 + 0.0129255i \(0.995886\pi\)
\(338\) 0.294987 2.78880i 0.0160452 0.151691i
\(339\) −3.93080 3.93080i −0.213492 0.213492i
\(340\) −0.123040 + 15.1807i −0.00667279 + 0.823291i
\(341\) 6.87549 6.87549i 0.372329 0.372329i
\(342\) −3.74877 + 3.03158i −0.202710 + 0.163929i
\(343\) −1.00000 −0.0539949
\(344\) −8.97542 17.7023i −0.483922 0.954445i
\(345\) 1.05225 1.59652i 0.0566510 0.0859539i
\(346\) 7.34285 5.93805i 0.394754 0.319232i
\(347\) 20.8645 + 20.8645i 1.12007 + 1.12007i 0.991731 + 0.128335i \(0.0409634\pi\)
0.128335 + 0.991731i \(0.459037\pi\)
\(348\) 2.19224 + 0.469018i 0.117516 + 0.0251420i
\(349\) −0.488555 0.488555i −0.0261517 0.0261517i 0.693910 0.720062i \(-0.255887\pi\)
−0.720062 + 0.693910i \(0.755887\pi\)
\(350\) 6.75537 2.08925i 0.361090 0.111675i
\(351\) 7.65658 0.408678
\(352\) 18.1995 4.81185i 0.970038 0.256473i
\(353\) 23.3169i 1.24103i −0.784194 0.620516i \(-0.786923\pi\)
0.784194 0.620516i \(-0.213077\pi\)
\(354\) −0.461321 + 4.36132i −0.0245189 + 0.231802i
\(355\) 7.24655 + 35.2659i 0.384607 + 1.87172i
\(356\) 7.05508 32.9762i 0.373918 1.74773i
\(357\) 0.947446 + 0.947446i 0.0501442 + 0.0501442i
\(358\) 1.88877 + 2.33560i 0.0998244 + 0.123440i
\(359\) 14.5780i 0.769397i 0.923042 + 0.384699i \(0.125695\pi\)
−0.923042 + 0.384699i \(0.874305\pi\)
\(360\) 2.03709 17.8726i 0.107364 0.941969i
\(361\) 17.5633i 0.924386i
\(362\) −24.3666 + 19.7049i −1.28068 + 1.03567i
\(363\) 0.0207272 + 0.0207272i 0.00108790 + 0.00108790i
\(364\) 5.57221 3.60813i 0.292063 0.189117i
\(365\) 11.6376 2.39133i 0.609139 0.125168i
\(366\) 0.424229 + 0.0448730i 0.0221748 + 0.00234555i
\(367\) 24.7854i 1.29379i 0.762580 + 0.646894i \(0.223932\pi\)
−0.762580 + 0.646894i \(0.776068\pi\)
\(368\) −7.90719 3.54570i −0.412191 0.184832i
\(369\) −31.4385 −1.63662
\(370\) −17.4065 14.3112i −0.904919 0.744006i
\(371\) 1.62915 + 1.62915i 0.0845813 + 0.0845813i
\(372\) 1.93613 1.25368i 0.100384 0.0650005i
\(373\) −13.4261 13.4261i −0.695176 0.695176i 0.268190 0.963366i \(-0.413574\pi\)
−0.963366 + 0.268190i \(0.913574\pi\)
\(374\) 10.0457 + 12.4223i 0.519451 + 0.642340i
\(375\) −0.778811 + 4.34372i −0.0402176 + 0.224309i
\(376\) −6.50378 + 19.8818i −0.335407 + 1.02532i
\(377\) 9.42607 0.485468
\(378\) −2.05132 2.53661i −0.105508 0.130469i
\(379\) 22.2169 22.2169i 1.14121 1.14121i 0.152978 0.988230i \(-0.451114\pi\)
0.988230 0.152978i \(-0.0488863\pi\)
\(380\) −3.75949 3.82093i −0.192858 0.196009i
\(381\) −0.0925710 0.0925710i −0.00474255 0.00474255i
\(382\) −32.5725 3.44537i −1.66655 0.176280i
\(383\) 15.1410i 0.773670i −0.922149 0.386835i \(-0.873568\pi\)
0.922149 0.386835i \(-0.126432\pi\)
\(384\) 4.46054 0.212986i 0.227626 0.0108689i
\(385\) 4.09496 6.21310i 0.208699 0.316649i
\(386\) 1.40276 13.2617i 0.0713987 0.675002i
\(387\) −14.1127 + 14.1127i −0.717390 + 0.717390i
\(388\) −2.58045 + 12.0613i −0.131002 + 0.612319i
\(389\) −6.59187 + 6.59187i −0.334221 + 0.334221i −0.854187 0.519966i \(-0.825945\pi\)
0.519966 + 0.854187i \(0.325945\pi\)
\(390\) 0.402386 + 4.12336i 0.0203756 + 0.208794i
\(391\) 7.35427i 0.371921i
\(392\) −2.68825 0.879388i −0.135777 0.0444158i
\(393\) 2.72590 0.137503
\(394\) 16.2240 + 20.0622i 0.817355 + 1.01072i
\(395\) 6.69827 1.37638i 0.337027 0.0692534i
\(396\) −10.2889 15.8896i −0.517035 0.798484i
\(397\) 0.462411 0.462411i 0.0232078 0.0232078i −0.695408 0.718615i \(-0.744776\pi\)
0.718615 + 0.695408i \(0.244776\pi\)
\(398\) −0.772642 + 7.30455i −0.0387291 + 0.366144i
\(399\) −0.473102 −0.0236847
\(400\) 19.9974 + 0.324179i 0.999869 + 0.0162090i
\(401\) −17.4581 −0.871817 −0.435908 0.899991i \(-0.643573\pi\)
−0.435908 + 0.899991i \(0.643573\pi\)
\(402\) 0.389810 3.68526i 0.0194420 0.183804i
\(403\) 6.85770 6.85770i 0.341606 0.341606i
\(404\) 14.4426 9.35190i 0.718547 0.465274i
\(405\) −16.6948 + 3.43049i −0.829569 + 0.170463i
\(406\) −2.52539 3.12284i −0.125333 0.154984i
\(407\) −23.7139 −1.17545
\(408\) 1.71380 + 3.38014i 0.0848456 + 0.167342i
\(409\) 24.3263i 1.20286i −0.798926 0.601430i \(-0.794598\pi\)
0.798926 0.601430i \(-0.205402\pi\)
\(410\) −3.39496 34.7891i −0.167665 1.71811i
\(411\) −3.02910 + 3.02910i −0.149414 + 0.149414i
\(412\) 31.4211 + 6.72237i 1.54801 + 0.331188i
\(413\) 5.55555 5.55555i 0.273371 0.273371i
\(414\) −0.916626 + 8.66577i −0.0450497 + 0.425899i
\(415\) −9.50820 + 14.4264i −0.466739 + 0.708162i
\(416\) 18.1524 4.79940i 0.889996 0.235310i
\(417\) 6.46223i 0.316457i
\(418\) −5.60962 0.593361i −0.274376 0.0290222i
\(419\) −6.87681 6.87681i −0.335954 0.335954i 0.518888 0.854842i \(-0.326346\pi\)
−0.854842 + 0.518888i \(0.826346\pi\)
\(420\) 1.25826 1.23802i 0.0613966 0.0604093i
\(421\) −13.4535 + 13.4535i −0.655685 + 0.655685i −0.954356 0.298671i \(-0.903457\pi\)
0.298671 + 0.954356i \(0.403457\pi\)
\(422\) 14.0209 + 17.3379i 0.682526 + 0.843994i
\(423\) 21.0352 1.02277
\(424\) 2.94691 + 5.81222i 0.143114 + 0.282266i
\(425\) 6.69280 + 15.5979i 0.324649 + 0.756608i
\(426\) 5.65142 + 6.98841i 0.273812 + 0.338589i
\(427\) −0.540392 0.540392i −0.0261514 0.0261514i
\(428\) −18.6736 28.8385i −0.902620 1.39396i
\(429\) 3.08285 + 3.08285i 0.148841 + 0.148841i
\(430\) −17.1408 14.0928i −0.826602 0.679615i
\(431\) 36.7314 1.76929 0.884645 0.466266i \(-0.154401\pi\)
0.884645 + 0.466266i \(0.154401\pi\)
\(432\) −3.28379 8.62294i −0.157991 0.414871i
\(433\) 36.4368i 1.75104i −0.483182 0.875520i \(-0.660519\pi\)
0.483182 0.875520i \(-0.339481\pi\)
\(434\) −4.10923 0.434656i −0.197249 0.0208641i
\(435\) 2.45516 0.504496i 0.117716 0.0241887i
\(436\) −6.42050 9.91550i −0.307486 0.474866i
\(437\) 1.83616 + 1.83616i 0.0878352 + 0.0878352i
\(438\) 2.30614 1.86495i 0.110192 0.0891105i
\(439\) 22.3458i 1.06651i −0.845955 0.533255i \(-0.820969\pi\)
0.845955 0.533255i \(-0.179031\pi\)
\(440\) 16.4720 13.1013i 0.785272 0.624579i
\(441\) 2.84420i 0.135438i
\(442\) 10.0197 + 12.3901i 0.476589 + 0.589337i
\(443\) 20.0254 + 20.0254i 0.951435 + 0.951435i 0.998874 0.0474395i \(-0.0151061\pi\)
−0.0474395 + 0.998874i \(0.515106\pi\)
\(444\) −5.50090 1.17689i −0.261061 0.0558527i
\(445\) −7.58875 36.9312i −0.359741 1.75071i
\(446\) 1.30929 12.3780i 0.0619968 0.586117i
\(447\) 5.20423i 0.246152i
\(448\) −6.45335 4.72803i −0.304892 0.223378i
\(449\) 20.4015 0.962805 0.481403 0.876500i \(-0.340128\pi\)
0.481403 + 0.876500i \(0.340128\pi\)
\(450\) −5.94224 19.2137i −0.280120 0.905741i
\(451\) −26.0102 26.0102i −1.22477 1.22477i
\(452\) −5.89293 + 27.5442i −0.277180 + 1.29557i
\(453\) −5.15905 5.15905i −0.242393 0.242393i
\(454\) 0.915287 0.740179i 0.0429566 0.0347383i
\(455\) 4.08437 6.19702i 0.191478 0.290521i
\(456\) −1.27181 0.416040i −0.0595582 0.0194829i
\(457\) −11.8938 −0.556368 −0.278184 0.960528i \(-0.589733\pi\)
−0.278184 + 0.960528i \(0.589733\pi\)
\(458\) −26.9288 + 21.7769i −1.25830 + 1.01757i
\(459\) 5.53707 5.53707i 0.258448 0.258448i
\(460\) −9.68831 0.0785239i −0.451720 0.00366119i
\(461\) 18.8680 + 18.8680i 0.878772 + 0.878772i 0.993408 0.114636i \(-0.0365702\pi\)
−0.114636 + 0.993408i \(0.536570\pi\)
\(462\) 0.195397 1.84728i 0.00909071 0.0859434i
\(463\) 30.6387i 1.42390i 0.702229 + 0.711951i \(0.252188\pi\)
−0.702229 + 0.711951i \(0.747812\pi\)
\(464\) −4.04270 10.6158i −0.187678 0.492825i
\(465\) 1.41916 2.15323i 0.0658120 0.0998534i
\(466\) 24.9295 + 2.63693i 1.15483 + 0.122153i
\(467\) 8.47204 8.47204i 0.392039 0.392039i −0.483374 0.875414i \(-0.660589\pi\)
0.875414 + 0.483374i \(0.160589\pi\)
\(468\) −10.2622 15.8485i −0.474372 0.732597i
\(469\) −4.69437 + 4.69437i −0.216766 + 0.216766i
\(470\) 2.27153 + 23.2770i 0.104778 + 1.07369i
\(471\) 7.47483i 0.344422i
\(472\) 19.8202 10.0492i 0.912297 0.462552i
\(473\) −23.3519 −1.07372
\(474\) 1.32735 1.07341i 0.0609673 0.0493034i
\(475\) −5.56536 2.22335i −0.255356 0.102014i
\(476\) 1.42038 6.63901i 0.0651031 0.304299i
\(477\) 4.63364 4.63364i 0.212160 0.212160i
\(478\) 11.5374 + 1.22038i 0.527709 + 0.0558187i
\(479\) 5.79127 0.264610 0.132305 0.991209i \(-0.457762\pi\)
0.132305 + 0.991209i \(0.457762\pi\)
\(480\) 4.47121 2.22162i 0.204082 0.101403i
\(481\) −23.6525 −1.07846
\(482\) 26.0514 + 2.75560i 1.18661 + 0.125514i
\(483\) −0.604658 + 0.604658i −0.0275129 + 0.0275129i
\(484\) 0.0310736 0.145241i 0.00141244 0.00660188i
\(485\) 2.77564 + 13.5079i 0.126035 + 0.613361i
\(486\) −10.9181 + 8.82932i −0.495256 + 0.400506i
\(487\) −1.46355 −0.0663197 −0.0331599 0.999450i \(-0.510557\pi\)
−0.0331599 + 0.999450i \(0.510557\pi\)
\(488\) −0.977494 1.92792i −0.0442491 0.0872729i
\(489\) 1.68489i 0.0761936i
\(490\) −3.14733 + 0.307138i −0.142182 + 0.0138751i
\(491\) −2.47769 + 2.47769i −0.111817 + 0.111817i −0.760801 0.648985i \(-0.775194\pi\)
0.648985 + 0.760801i \(0.275194\pi\)
\(492\) −4.74273 7.32443i −0.213819 0.330211i
\(493\) 6.81673 6.81673i 0.307010 0.307010i
\(494\) −5.59511 0.591825i −0.251736 0.0266275i
\(495\) −17.6713 11.6469i −0.794267 0.523490i
\(496\) −10.6644 4.78207i −0.478845 0.214721i
\(497\) 16.1009i 0.722224i
\(498\) −0.453698 + 4.28926i −0.0203307 + 0.192206i
\(499\) 26.8709 + 26.8709i 1.20291 + 1.20291i 0.973279 + 0.229627i \(0.0737506\pi\)
0.229627 + 0.973279i \(0.426249\pi\)
\(500\) 20.6197 8.65037i 0.922140 0.386856i
\(501\) 1.21594 1.21594i 0.0543244 0.0543244i
\(502\) 4.56649 3.69285i 0.203812 0.164820i
\(503\) 33.7090 1.50301 0.751506 0.659726i \(-0.229328\pi\)
0.751506 + 0.659726i \(0.229328\pi\)
\(504\) −2.50116 + 7.64593i −0.111410 + 0.340577i
\(505\) 10.5863 16.0621i 0.471083 0.714752i
\(506\) −7.92785 + 6.41114i −0.352436 + 0.285010i
\(507\) −0.553453 0.553453i −0.0245797 0.0245797i
\(508\) −0.138780 + 0.648670i −0.00615735 + 0.0287801i
\(509\) −13.1713 13.1713i −0.583808 0.583808i 0.352139 0.935948i \(-0.385454\pi\)
−0.935948 + 0.352139i \(0.885454\pi\)
\(510\) 3.27292 + 2.69093i 0.144927 + 0.119156i
\(511\) −5.31323 −0.235043
\(512\) −13.1904 18.3851i −0.582941 0.812515i
\(513\) 2.76490i 0.122073i
\(514\) −0.225331 + 2.13028i −0.00993894 + 0.0939626i
\(515\) 35.1896 7.23088i 1.55064 0.318631i
\(516\) −5.41693 1.15892i −0.238467 0.0510188i
\(517\) 17.4031 + 17.4031i 0.765390 + 0.765390i
\(518\) 6.33688 + 7.83603i 0.278427 + 0.344295i
\(519\) 2.63567i 0.115693i
\(520\) 16.4294 13.0674i 0.720476 0.573043i
\(521\) 27.9324i 1.22374i 0.790958 + 0.611871i \(0.209583\pi\)
−0.790958 + 0.611871i \(0.790417\pi\)
\(522\) −8.88200 + 7.18274i −0.388754 + 0.314380i
\(523\) 7.58361 + 7.58361i 0.331608 + 0.331608i 0.853197 0.521589i \(-0.174660\pi\)
−0.521589 + 0.853197i \(0.674660\pi\)
\(524\) −7.50727 11.5939i −0.327957 0.506480i
\(525\) 0.732163 1.83271i 0.0319542 0.0799860i
\(526\) −23.2642 2.46078i −1.01437 0.107295i
\(527\) 9.91867i 0.432064i
\(528\) 2.14976 4.79413i 0.0935561 0.208638i
\(529\) −18.3065 −0.795936
\(530\) 5.62784 + 4.62710i 0.244458 + 0.200988i
\(531\) −15.8011 15.8011i −0.685710 0.685710i
\(532\) 1.30295 + 2.01221i 0.0564899 + 0.0872402i
\(533\) −25.9429 25.9429i −1.12371 1.12371i
\(534\) −5.91829 7.31841i −0.256110 0.316699i
\(535\) −32.0722 21.1383i −1.38660 0.913888i
\(536\) −16.7478 + 8.49145i −0.723394 + 0.366775i
\(537\) 0.838349 0.0361774
\(538\) −9.13519 11.2963i −0.393846 0.487020i
\(539\) −2.35311 + 2.35311i −0.101356 + 0.101356i
\(540\) −7.23526 7.35350i −0.311356 0.316444i
\(541\) −10.1790 10.1790i −0.437631 0.437631i 0.453583 0.891214i \(-0.350146\pi\)
−0.891214 + 0.453583i \(0.850146\pi\)
\(542\) −14.6285 1.54734i −0.628348 0.0664638i
\(543\) 8.74623i 0.375337i
\(544\) 9.65661 16.5982i 0.414024 0.711644i
\(545\) −11.0273 7.26795i −0.472359 0.311325i
\(546\) 0.194892 1.84250i 0.00834060 0.0788519i
\(547\) 16.9073 16.9073i 0.722905 0.722905i −0.246291 0.969196i \(-0.579212\pi\)
0.969196 + 0.246291i \(0.0792118\pi\)
\(548\) 21.2257 + 4.54113i 0.906718 + 0.193988i
\(549\) −1.53699 + 1.53699i −0.0655969 + 0.0655969i
\(550\) 10.9799 20.8124i 0.468185 0.887442i
\(551\) 3.40389i 0.145011i
\(552\) −2.15720 + 1.09374i −0.0918164 + 0.0465527i
\(553\) −3.05814 −0.130046
\(554\) 3.80879 + 4.70985i 0.161820 + 0.200102i
\(555\) −6.16066 + 1.26591i −0.261505 + 0.0537350i
\(556\) 27.4853 17.7973i 1.16564 0.754775i
\(557\) −8.36638 + 8.36638i −0.354495 + 0.354495i −0.861779 0.507284i \(-0.830649\pi\)
0.507284 + 0.861779i \(0.330649\pi\)
\(558\) −1.23625 + 11.6875i −0.0523346 + 0.494771i
\(559\) −23.2915 −0.985124
\(560\) −8.73089 1.94206i −0.368947 0.0820670i
\(561\) 4.45889 0.188255
\(562\) 3.96409 37.4764i 0.167215 1.58085i
\(563\) 31.3813 31.3813i 1.32256 1.32256i 0.410870 0.911694i \(-0.365225\pi\)
0.911694 0.410870i \(-0.134775\pi\)
\(564\) 3.17331 + 4.90070i 0.133620 + 0.206357i
\(565\) 6.33869 + 30.8477i 0.266671 + 1.29777i
\(566\) 2.26303 + 2.79840i 0.0951221 + 0.117626i
\(567\) 7.62211 0.320099
\(568\) 14.1589 43.2832i 0.594095 1.81612i
\(569\) 24.9959i 1.04788i 0.851754 + 0.523941i \(0.175539\pi\)
−0.851754 + 0.523941i \(0.824461\pi\)
\(570\) −1.48901 + 0.145307i −0.0623676 + 0.00608626i
\(571\) −10.5685 + 10.5685i −0.442279 + 0.442279i −0.892777 0.450498i \(-0.851246\pi\)
0.450498 + 0.892777i \(0.351246\pi\)
\(572\) 4.62171 21.6023i 0.193243 0.903239i
\(573\) −6.46419 + 6.46419i −0.270045 + 0.270045i
\(574\) −1.64432 + 15.5453i −0.0686324 + 0.648850i
\(575\) −9.95453 + 4.27133i −0.415132 + 0.178127i
\(576\) −13.4475 + 18.3547i −0.560311 + 0.764777i
\(577\) 11.8907i 0.495014i 0.968886 + 0.247507i \(0.0796114\pi\)
−0.968886 + 0.247507i \(0.920389\pi\)
\(578\) −7.70198 0.814681i −0.320360 0.0338863i
\(579\) −2.63186 2.63186i −0.109376 0.109376i
\(580\) −8.90738 9.05295i −0.369859 0.375903i
\(581\) 5.46375 5.46375i 0.226675 0.226675i
\(582\) 2.16466 + 2.67677i 0.0897281 + 0.110956i
\(583\) 7.66715 0.317541
\(584\) −14.2833 4.67239i −0.591046 0.193345i
\(585\) −17.6256 11.6168i −0.728729 0.480294i
\(586\) 2.72030 + 3.36385i 0.112374 + 0.138959i
\(587\) 16.0540 + 16.0540i 0.662620 + 0.662620i 0.955997 0.293377i \(-0.0947791\pi\)
−0.293377 + 0.955997i \(0.594779\pi\)
\(588\) −0.662632 + 0.429069i −0.0273265 + 0.0176945i
\(589\) 2.47642 + 2.47642i 0.102039 + 0.102039i
\(590\) 15.7788 19.1914i 0.649603 0.790099i
\(591\) 7.20122 0.296218
\(592\) 10.1442 + 26.6378i 0.416924 + 1.09481i
\(593\) 16.8255i 0.690941i −0.938430 0.345471i \(-0.887719\pi\)
0.938430 0.345471i \(-0.112281\pi\)
\(594\) −10.7959 1.14194i −0.442961 0.0468545i
\(595\) −1.52782 7.43527i −0.0626347 0.304816i
\(596\) 22.1348 14.3327i 0.906675 0.587091i
\(597\) 1.44963 + 1.44963i 0.0593293 + 0.0593293i
\(598\) −7.90734 + 6.39455i −0.323355 + 0.261492i
\(599\) 39.0027i 1.59361i 0.604238 + 0.796804i \(0.293478\pi\)
−0.604238 + 0.796804i \(0.706522\pi\)
\(600\) 3.57990 4.28292i 0.146149 0.174850i
\(601\) 40.5397i 1.65365i 0.562459 + 0.826825i \(0.309855\pi\)
−0.562459 + 0.826825i \(0.690145\pi\)
\(602\) 6.24015 + 7.71642i 0.254330 + 0.314498i
\(603\) 13.3517 + 13.3517i 0.543725 + 0.543725i
\(604\) −7.73428 + 36.1509i −0.314704 + 1.47096i
\(605\) −0.0334241 0.162661i −0.00135888 0.00661311i
\(606\) 0.505140 4.77558i 0.0205199 0.193995i
\(607\) 25.2830i 1.02620i 0.858328 + 0.513102i \(0.171504\pi\)
−0.858328 + 0.513102i \(0.828496\pi\)
\(608\) 1.73313 + 6.55511i 0.0702879 + 0.265845i
\(609\) −1.12092 −0.0454221
\(610\) −1.86677 1.53482i −0.0755831 0.0621429i
\(611\) 17.3581 + 17.3581i 0.702234 + 0.702234i
\(612\) −18.8827 4.03986i −0.763288 0.163302i
\(613\) −5.73016 5.73016i −0.231439 0.231439i 0.581854 0.813293i \(-0.302327\pi\)
−0.813293 + 0.581854i \(0.802327\pi\)
\(614\) 27.9314 22.5877i 1.12722 0.911567i
\(615\) −8.14572 5.36873i −0.328467 0.216488i
\(616\) −8.39504 + 4.25645i −0.338246 + 0.171497i
\(617\) 38.7107 1.55844 0.779218 0.626753i \(-0.215617\pi\)
0.779218 + 0.626753i \(0.215617\pi\)
\(618\) 6.97329 5.63920i 0.280507 0.226842i
\(619\) −11.8179 + 11.8179i −0.475001 + 0.475001i −0.903529 0.428528i \(-0.859032\pi\)
0.428528 + 0.903529i \(0.359032\pi\)
\(620\) −13.0666 0.105905i −0.524767 0.00425324i
\(621\) 3.53374 + 3.53374i 0.141804 + 0.141804i
\(622\) −2.53821 + 23.9962i −0.101773 + 0.962160i
\(623\) 16.8612i 0.675530i
\(624\) 2.14419 4.78172i 0.0858364 0.191422i
\(625\) 17.2257 18.1184i 0.689028 0.724735i
\(626\) 17.1468 + 1.81371i 0.685324 + 0.0724905i
\(627\) −1.11326 + 1.11326i −0.0444594 + 0.0444594i
\(628\) 31.7921 20.5861i 1.26864 0.821474i
\(629\) −17.1050 + 17.1050i −0.682020 + 0.682020i
\(630\) 0.873562 + 8.95164i 0.0348036 + 0.356642i
\(631\) 3.31829i 0.132099i −0.997816 0.0660495i \(-0.978960\pi\)
0.997816 0.0660495i \(-0.0210395\pi\)
\(632\) −8.22105 2.68930i −0.327016 0.106974i
\(633\) 6.22332 0.247355
\(634\) 20.6447 16.6950i 0.819905 0.663045i
\(635\) 0.149277 + 0.726469i 0.00592389 + 0.0288290i
\(636\) 1.77855 + 0.380510i 0.0705239 + 0.0150882i
\(637\) −2.34702 + 2.34702i −0.0929924 + 0.0929924i
\(638\) −13.2909 1.40585i −0.526193 0.0556583i
\(639\) −45.7942 −1.81159
\(640\) −21.7630 12.8986i −0.860257 0.509861i
\(641\) 27.1752 1.07336 0.536678 0.843787i \(-0.319679\pi\)
0.536678 + 0.843787i \(0.319679\pi\)
\(642\) −9.53572 1.00865i −0.376345 0.0398081i
\(643\) −21.5065 + 21.5065i −0.848133 + 0.848133i −0.989900 0.141767i \(-0.954722\pi\)
0.141767 + 0.989900i \(0.454722\pi\)
\(644\) 4.23700 + 0.906484i 0.166961 + 0.0357205i
\(645\) −6.06662 + 1.24659i −0.238873 + 0.0490844i
\(646\) −4.47425 + 3.61826i −0.176037 + 0.142359i
\(647\) 6.44417 0.253347 0.126673 0.991944i \(-0.459570\pi\)
0.126673 + 0.991944i \(0.459570\pi\)
\(648\) 20.4901 + 6.70279i 0.804928 + 0.263311i
\(649\) 26.1456i 1.02631i
\(650\) 10.9515 20.7585i 0.429553 0.814216i
\(651\) −0.815499 + 0.815499i −0.0319619 + 0.0319619i
\(652\) −7.16623 + 4.64029i −0.280651 + 0.181728i
\(653\) −26.3507 + 26.3507i −1.03118 + 1.03118i −0.0316854 + 0.999498i \(0.510087\pi\)
−0.999498 + 0.0316854i \(0.989913\pi\)
\(654\) −3.27865 0.346801i −0.128205 0.0135610i
\(655\) −12.8939 8.49816i −0.503805 0.332051i
\(656\) −18.0907 + 40.3437i −0.706324 + 1.57516i
\(657\) 15.1119i 0.589571i
\(658\) 1.10019 10.4012i 0.0428900 0.405482i
\(659\) −23.1868 23.1868i −0.903231 0.903231i 0.0924832 0.995714i \(-0.470520\pi\)
−0.995714 + 0.0924832i \(0.970520\pi\)
\(660\) 0.0476090 5.87402i 0.00185318 0.228646i
\(661\) −0.247738 + 0.247738i −0.00963589 + 0.00963589i −0.711908 0.702272i \(-0.752169\pi\)
0.702272 + 0.711908i \(0.252169\pi\)
\(662\) 17.0381 13.7784i 0.662203 0.535514i
\(663\) 4.44735 0.172721
\(664\) 19.4927 9.88316i 0.756462 0.383541i
\(665\) 2.23783 + 1.47492i 0.0867795 + 0.0571951i
\(666\) 22.2873 18.0234i 0.863614 0.698392i
\(667\) 4.35042 + 4.35042i 0.168449 + 0.168449i
\(668\) −8.52046 1.82291i −0.329666 0.0705304i
\(669\) −2.45649 2.45649i −0.0949734 0.0949734i
\(670\) −13.3329 + 16.2165i −0.515094 + 0.626499i
\(671\) −2.54321 −0.0981794
\(672\) −2.15864 + 0.570732i −0.0832713 + 0.0220165i
\(673\) 45.2564i 1.74451i 0.489056 + 0.872253i \(0.337342\pi\)
−0.489056 + 0.872253i \(0.662658\pi\)
\(674\) 0.0705951 0.667405i 0.00271922 0.0257075i
\(675\) −10.7107 4.27891i −0.412256 0.164695i
\(676\) −0.829720 + 3.87820i −0.0319123 + 0.149161i
\(677\) 32.0109 + 32.0109i 1.23028 + 1.23028i 0.963856 + 0.266424i \(0.0858422\pi\)
0.266424 + 0.963856i \(0.414158\pi\)
\(678\) 4.94341 + 6.11289i 0.189850 + 0.234764i
\(679\) 6.16712i 0.236672i
\(680\) 2.43131 21.3314i 0.0932367 0.818022i
\(681\) 0.328537i 0.0125896i
\(682\) −10.6923 + 8.64668i −0.409428 + 0.331098i
\(683\) 27.9310 + 27.9310i 1.06875 + 1.06875i 0.997455 + 0.0712942i \(0.0227129\pi\)
0.0712942 + 0.997455i \(0.477287\pi\)
\(684\) 5.72313 3.70585i 0.218829 0.141697i
\(685\) 23.7715 4.88464i 0.908261 0.186632i
\(686\) 1.40637 + 0.148759i 0.0536954 + 0.00567966i
\(687\) 9.66593i 0.368778i
\(688\) 9.98936 + 26.2312i 0.380841 + 1.00005i
\(689\) 7.64730 0.291339
\(690\) −1.71734 + 2.08877i −0.0653781 + 0.0795180i
\(691\) 8.48560 + 8.48560i 0.322808 + 0.322808i 0.849843 0.527036i \(-0.176697\pi\)
−0.527036 + 0.849843i \(0.676697\pi\)
\(692\) −11.2101 + 7.25877i −0.426144 + 0.275937i
\(693\) 6.69273 + 6.69273i 0.254236 + 0.254236i
\(694\) −26.2394 32.4470i −0.996034 1.23167i
\(695\) 20.1464 30.5672i 0.764197 1.15948i
\(696\) −3.01332 0.985727i −0.114220 0.0373639i
\(697\) −37.5227 −1.42127
\(698\) 0.614411 + 0.759765i 0.0232558 + 0.0287575i
\(699\) 4.94739 4.94739i 0.187127 0.187127i
\(700\) −9.81133 + 1.93333i −0.370834 + 0.0730728i
\(701\) −13.1810 13.1810i −0.497841 0.497841i 0.412924 0.910765i \(-0.364507\pi\)
−0.910765 + 0.412924i \(0.864507\pi\)
\(702\) −10.7680 1.13899i −0.406411 0.0429883i
\(703\) 8.54127i 0.322140i
\(704\) −26.3110 + 4.05989i −0.991634 + 0.153013i
\(705\) 5.45021 + 3.59216i 0.205267 + 0.135288i
\(706\) −3.46860 + 32.7921i −0.130543 + 1.23415i
\(707\) −6.08324 + 6.08324i −0.228784 + 0.228784i
\(708\) 1.29757 6.06500i 0.0487658 0.227936i
\(709\) −13.3068 + 13.3068i −0.499747 + 0.499747i −0.911359 0.411612i \(-0.864966\pi\)
0.411612 + 0.911359i \(0.364966\pi\)
\(710\) −4.94519 50.6748i −0.185590 1.90179i
\(711\) 8.69799i 0.326200i
\(712\) −14.8275 + 45.3271i −0.555686 + 1.69871i
\(713\) 6.33007 0.237063
\(714\) −1.19152 1.47340i −0.0445914 0.0551406i
\(715\) −4.97131 24.1932i −0.185916 0.904776i
\(716\) −2.30886 3.56569i −0.0862861 0.133256i
\(717\) 2.28967 2.28967i 0.0855091 0.0855091i
\(718\) 2.16861 20.5020i 0.0809319 0.765129i
\(719\) 2.29721 0.0856715 0.0428357 0.999082i \(-0.486361\pi\)
0.0428357 + 0.999082i \(0.486361\pi\)
\(720\) −5.52361 + 24.8324i −0.205853 + 0.925450i
\(721\) −16.0661 −0.598332
\(722\) −2.61271 + 24.7005i −0.0972350 + 0.919258i
\(723\) 5.17004 5.17004i 0.192276 0.192276i
\(724\) 37.1997 24.0876i 1.38252 0.895208i
\(725\) −13.1861 5.26780i −0.489718 0.195641i
\(726\) −0.0260667 0.0322335i −0.000967428 0.00119630i
\(727\) −27.4131 −1.01670 −0.508348 0.861152i \(-0.669743\pi\)
−0.508348 + 0.861152i \(0.669743\pi\)
\(728\) −8.37332 + 4.24543i −0.310336 + 0.157346i
\(729\) 18.9474i 0.701754i
\(730\) −16.7225 + 1.63189i −0.618926 + 0.0603990i
\(731\) −16.8439 + 16.8439i −0.622993 + 0.622993i
\(732\) −0.589947 0.126216i −0.0218051 0.00466508i
\(733\) 13.8814 13.8814i 0.512721 0.512721i −0.402638 0.915359i \(-0.631907\pi\)
0.915359 + 0.402638i \(0.131907\pi\)
\(734\) 3.68706 34.8574i 0.136092 1.28661i
\(735\) −0.485702 + 0.736933i −0.0179154 + 0.0271822i
\(736\) 10.5930 + 6.16282i 0.390462 + 0.227165i
\(737\) 22.0927i 0.813796i
\(738\) 44.2141 + 4.67677i 1.62754 + 0.172154i
\(739\) 36.0336 + 36.0336i 1.32552 + 1.32552i 0.909235 + 0.416283i \(0.136667\pi\)
0.416283 + 0.909235i \(0.363333\pi\)
\(740\) 22.3510 + 22.7162i 0.821638 + 0.835066i
\(741\) −1.11038 + 1.11038i −0.0407908 + 0.0407908i
\(742\) −2.04883 2.53354i −0.0752151 0.0930091i
\(743\) −38.8070 −1.42369 −0.711845 0.702337i \(-0.752140\pi\)
−0.711845 + 0.702337i \(0.752140\pi\)
\(744\) −2.90941 + 1.47512i −0.106664 + 0.0540807i
\(745\) 16.2245 24.6167i 0.594421 0.901887i
\(746\) 16.8847 + 20.8792i 0.618194 + 0.764444i
\(747\) −15.5400 15.5400i −0.568580 0.568580i
\(748\) −12.2800 18.9647i −0.449002 0.693416i
\(749\) 12.1468 + 12.1468i 0.443835 + 0.443835i
\(750\) 1.74146 5.99301i 0.0635892 0.218834i
\(751\) 23.4759 0.856648 0.428324 0.903625i \(-0.359104\pi\)
0.428324 + 0.903625i \(0.359104\pi\)
\(752\) 12.1043 26.9936i 0.441398 0.984354i
\(753\) 1.63911i 0.0597326i
\(754\) −13.2565 1.40222i −0.482774 0.0510657i
\(755\) 8.31933 + 40.4866i 0.302771 + 1.47346i
\(756\) 2.50757 + 3.87256i 0.0911993 + 0.140844i
\(757\) −22.9312 22.9312i −0.833449 0.833449i 0.154538 0.987987i \(-0.450611\pi\)
−0.987987 + 0.154538i \(0.950611\pi\)
\(758\) −34.5502 + 27.9402i −1.25492 + 1.01483i
\(759\) 2.84565i 0.103291i
\(760\) 4.71882 + 5.93289i 0.171170 + 0.215208i
\(761\) 36.3457i 1.31753i 0.752348 + 0.658765i \(0.228921\pi\)
−0.752348 + 0.658765i \(0.771079\pi\)
\(762\) 0.116418 + 0.143960i 0.00421738 + 0.00521511i
\(763\) 4.17642 + 4.17642i 0.151197 + 0.151197i
\(764\) 45.2963 + 9.69091i 1.63876 + 0.350605i
\(765\) −21.1474 + 4.34545i −0.764587 + 0.157110i
\(766\) −2.25237 + 21.2938i −0.0813813 + 0.769378i
\(767\) 26.0780i 0.941621i
\(768\) −6.30485 0.364010i −0.227507 0.0131351i
\(769\) −3.98219 −0.143601 −0.0718007 0.997419i \(-0.522875\pi\)
−0.0718007 + 0.997419i \(0.522875\pi\)
\(770\) −6.68328 + 8.12874i −0.240849 + 0.292939i
\(771\) 0.422766 + 0.422766i 0.0152255 + 0.0152255i
\(772\) −3.94560 + 18.4421i −0.142005 + 0.663747i
\(773\) −35.2651 35.2651i −1.26840 1.26840i −0.946916 0.321482i \(-0.895819\pi\)
−0.321482 0.946916i \(-0.604181\pi\)
\(774\) 21.9471 17.7483i 0.788871 0.637949i
\(775\) −13.4256 + 5.76073i −0.482263 + 0.206931i
\(776\) 5.42329 16.5787i 0.194685 0.595142i
\(777\) 2.81269 0.100905
\(778\) 10.2512 8.28999i 0.367523 0.297211i
\(779\) 9.36836 9.36836i 0.335656 0.335656i
\(780\) 0.0474858 5.85882i 0.00170026 0.209779i
\(781\) −37.8872 37.8872i −1.35571 1.35571i
\(782\) −1.09402 + 10.3428i −0.0391219 + 0.369858i
\(783\) 6.55091i 0.234110i
\(784\) 3.64985 + 1.63664i 0.130352 + 0.0584516i
\(785\) 23.3032 35.3569i 0.831729 1.26194i
\(786\) −3.83362 0.405503i −0.136741 0.0144638i
\(787\) 0.963947 0.963947i 0.0343610 0.0343610i −0.689718 0.724079i \(-0.742265\pi\)
0.724079 + 0.689718i \(0.242265\pi\)
\(788\) −19.8325 30.6284i −0.706505 1.09109i
\(789\) −4.61691 + 4.61691i −0.164366 + 0.164366i
\(790\) −9.62498 + 0.939271i −0.342441 + 0.0334178i
\(791\) 14.0838i 0.500761i
\(792\) 12.1062 + 23.8772i 0.430175 + 0.848440i
\(793\) −2.53662 −0.0900781
\(794\) −0.719108 + 0.581532i −0.0255202 + 0.0206378i
\(795\) 1.99186 0.409294i 0.0706439 0.0145161i
\(796\) 2.17324 10.1579i 0.0770284 0.360039i
\(797\) −6.59993 + 6.59993i −0.233782 + 0.233782i −0.814269 0.580488i \(-0.802862\pi\)
0.580488 + 0.814269i \(0.302862\pi\)
\(798\) 0.665355 + 0.0703783i 0.0235533 + 0.00249136i
\(799\) 25.1060 0.888186
\(800\) −28.0754 3.43071i −0.992617 0.121294i
\(801\) 47.9567 1.69447
\(802\) 24.5525 + 2.59706i 0.866980 + 0.0917052i
\(803\) −12.5026 + 12.5026i −0.441208 + 0.441208i
\(804\) −1.09643 + 5.12484i −0.0386682 + 0.180739i
\(805\) 4.74517 0.975054i 0.167245 0.0343661i
\(806\) −10.6646 + 8.62430i −0.375644 + 0.303778i
\(807\) −4.05475 −0.142734
\(808\) −21.7028 + 11.0037i −0.763502 + 0.387110i
\(809\) 13.0495i 0.458796i −0.973333 0.229398i \(-0.926324\pi\)
0.973333 0.229398i \(-0.0736757\pi\)
\(810\) 23.9893 2.34104i 0.842897 0.0822557i
\(811\) −22.0720 + 22.0720i −0.775053 + 0.775053i −0.978985 0.203932i \(-0.934628\pi\)
0.203932 + 0.978985i \(0.434628\pi\)
\(812\) 3.08708 + 4.76754i 0.108335 + 0.167308i
\(813\) −2.90311 + 2.90311i −0.101816 + 0.101816i
\(814\) 33.3504 + 3.52766i 1.16893 + 0.123644i
\(815\) −5.25277 + 7.96978i −0.183996 + 0.279169i
\(816\) −1.90740 5.00867i −0.0667724 0.175338i
\(817\) 8.41089i 0.294260i
\(818\) −3.61877 + 34.2118i −0.126527 + 1.19619i
\(819\) 6.67541 + 6.67541i 0.233258 + 0.233258i
\(820\) −0.400641 + 49.4313i −0.0139910 + 1.72622i
\(821\) 2.56931 2.56931i 0.0896695 0.0896695i −0.660849 0.750519i \(-0.729804\pi\)
0.750519 + 0.660849i \(0.229804\pi\)
\(822\) 4.71063 3.80942i 0.164302 0.132869i
\(823\) 12.4199 0.432930 0.216465 0.976290i \(-0.430547\pi\)
0.216465 + 0.976290i \(0.430547\pi\)
\(824\) −43.1896 14.1283i −1.50458 0.492183i
\(825\) −2.58971 6.03543i −0.0901620 0.210127i
\(826\) −8.63958 + 6.98670i −0.300609 + 0.243098i
\(827\) −12.7989 12.7989i −0.445062 0.445062i 0.448647 0.893709i \(-0.351906\pi\)
−0.893709 + 0.448647i \(0.851906\pi\)
\(828\) 2.57823 12.0509i 0.0895995 0.418798i
\(829\) 14.7686 + 14.7686i 0.512934 + 0.512934i 0.915424 0.402491i \(-0.131855\pi\)
−0.402491 + 0.915424i \(0.631855\pi\)
\(830\) 15.5181 18.8743i 0.538641 0.655138i
\(831\) 1.69057 0.0586453
\(832\) −26.2429 + 4.04938i −0.909810 + 0.140387i
\(833\) 3.39463i 0.117617i
\(834\) 0.961317 9.08827i 0.0332877 0.314701i
\(835\) −9.54237 + 1.96080i −0.330227 + 0.0678562i
\(836\) 7.80092 + 1.66897i 0.269801 + 0.0577224i
\(837\) 4.76595 + 4.76595i 0.164735 + 0.164735i
\(838\) 8.64834 + 10.6943i 0.298752 + 0.369429i
\(839\) 28.4351i 0.981688i −0.871247 0.490844i \(-0.836688\pi\)
0.871247 0.490844i \(-0.163312\pi\)
\(840\) −1.95374 + 1.55394i −0.0674103 + 0.0536160i
\(841\) 20.9351i 0.721901i
\(842\) 20.9219 16.9193i 0.721018 0.583077i
\(843\) −7.43741 7.43741i −0.256158 0.256158i
\(844\) −17.1393 26.4692i −0.589961 0.911106i
\(845\) 0.892483 + 4.34333i 0.0307023 + 0.149415i
\(846\) −29.5832 3.12918i −1.01709 0.107583i
\(847\) 0.0742641i 0.00255174i
\(848\) −3.27981 8.61250i −0.112629 0.295754i
\(849\) 1.00447 0.0344733
\(850\) −7.09221 22.9320i −0.243261 0.786560i
\(851\) −10.9163 10.9163i −0.374207 0.374207i
\(852\) −6.90839 10.6690i −0.236677 0.365513i
\(853\) 31.0724 + 31.0724i 1.06390 + 1.06390i 0.997814 + 0.0660853i \(0.0210510\pi\)
0.0660853 + 0.997814i \(0.478949\pi\)
\(854\) 0.679602 + 0.840378i 0.0232555 + 0.0287572i
\(855\) 4.19499 6.36486i 0.143466 0.217674i
\(856\) 21.9719 + 43.3354i 0.750984 + 1.48117i
\(857\) −43.7236 −1.49357 −0.746785 0.665066i \(-0.768403\pi\)
−0.746785 + 0.665066i \(0.768403\pi\)
\(858\) −3.87701 4.79422i −0.132359 0.163672i
\(859\) −8.83027 + 8.83027i −0.301285 + 0.301285i −0.841516 0.540231i \(-0.818337\pi\)
0.540231 + 0.841516i \(0.318337\pi\)
\(860\) 22.0098 + 22.3695i 0.750528 + 0.762794i
\(861\) 3.08506 + 3.08506i 0.105139 + 0.105139i
\(862\) −51.6579 5.46414i −1.75947 0.186109i
\(863\) 22.0584i 0.750876i −0.926848 0.375438i \(-0.877492\pi\)
0.926848 0.375438i \(-0.122508\pi\)
\(864\) 3.33548 + 12.6155i 0.113475 + 0.429189i
\(865\) −8.21687 + 12.4671i −0.279382 + 0.423893i
\(866\) −5.42031 + 51.2435i −0.184190 + 1.74133i
\(867\) −1.52850 + 1.52850i −0.0519106 + 0.0519106i
\(868\) 5.71443 + 1.22257i 0.193960 + 0.0414968i
\(869\) −7.19615 + 7.19615i −0.244113 + 0.244113i
\(870\) −3.52791 + 0.344278i −0.119607 + 0.0116721i
\(871\) 22.0356i 0.746646i
\(872\) 7.55456 + 14.8999i 0.255830 + 0.504576i
\(873\) −17.5405 −0.593657
\(874\) −2.30916 2.85545i −0.0781087 0.0965872i
\(875\) −9.17682 + 6.38640i −0.310233 + 0.215900i
\(876\) −3.52072 + 2.27974i −0.118954 + 0.0770252i
\(877\) 30.7374 30.7374i 1.03793 1.03793i 0.0386778 0.999252i \(-0.487685\pi\)
0.999252 0.0386778i \(-0.0123146\pi\)
\(878\) −3.32415 + 31.4265i −0.112185 + 1.06059i
\(879\) 1.20743 0.0407257
\(880\) −25.1146 + 15.9749i −0.846614 + 0.538513i
\(881\) 18.1801 0.612504 0.306252 0.951951i \(-0.400925\pi\)
0.306252 + 0.951951i \(0.400925\pi\)
\(882\) 0.423102 4.00000i 0.0142466 0.134687i
\(883\) 14.4743 14.4743i 0.487100 0.487100i −0.420290 0.907390i \(-0.638071\pi\)
0.907390 + 0.420290i \(0.138071\pi\)
\(884\) −12.2482 18.9156i −0.411953 0.636200i
\(885\) −1.39573 6.79241i −0.0469168 0.228324i
\(886\) −25.1841 31.1420i −0.846076 1.04624i
\(887\) 50.3891 1.69190 0.845950 0.533262i \(-0.179034\pi\)
0.845950 + 0.533262i \(0.179034\pi\)
\(888\) 7.56122 + 2.47345i 0.253738 + 0.0830035i
\(889\) 0.331675i 0.0111240i
\(890\) 5.17871 + 53.0677i 0.173591 + 1.77883i
\(891\) 17.9357 17.9357i 0.600868 0.600868i
\(892\) −3.68270 + 17.2133i −0.123306 + 0.576344i
\(893\) −6.26827 + 6.26827i −0.209760 + 0.209760i
\(894\) 0.774178 7.31907i 0.0258924 0.244786i
\(895\) −3.96551 2.61361i −0.132552 0.0873633i
\(896\) 8.37245 + 7.60934i 0.279704 + 0.254210i
\(897\) 2.83829i 0.0947677i
\(898\) −28.6920 3.03491i −0.957464 0.101276i
\(899\) 5.86739 + 5.86739i 0.195689 + 0.195689i
\(900\) 5.49877 + 27.9054i 0.183292 + 0.930181i
\(901\) 5.53036 5.53036i 0.184243 0.184243i
\(902\) 32.7107 + 40.4492i 1.08915 + 1.34681i
\(903\) 2.76976 0.0921718
\(904\) 12.3851 37.8606i 0.411922 1.25923i
\(905\) 27.2669 41.3709i 0.906384 1.37521i
\(906\) 6.48806 + 8.02297i 0.215551 + 0.266545i
\(907\) −7.63309 7.63309i −0.253453 0.253453i 0.568932 0.822385i \(-0.307357\pi\)
−0.822385 + 0.568932i \(0.807357\pi\)
\(908\) −1.39734 + 0.904807i −0.0463723 + 0.0300271i
\(909\) 17.3020 + 17.3020i 0.573871 + 0.573871i
\(910\) −6.66599 + 8.10770i −0.220975 + 0.268768i
\(911\) 27.1867 0.900736 0.450368 0.892843i \(-0.351293\pi\)
0.450368 + 0.892843i \(0.351293\pi\)
\(912\) 1.72675 + 0.774299i 0.0571784 + 0.0256396i
\(913\) 25.7136i 0.850997i
\(914\) 16.7271 + 1.76931i 0.553282 + 0.0585237i
\(915\) −0.660702 + 0.135763i −0.0218421 + 0.00448820i
\(916\) 41.1113 26.6205i 1.35836 0.879565i
\(917\) 4.88335 + 4.88335i 0.161262 + 0.161262i
\(918\) −8.61084 + 6.96346i −0.284200 + 0.229829i
\(919\) 16.2788i 0.536987i 0.963282 + 0.268493i \(0.0865258\pi\)
−0.963282 + 0.268493i \(0.913474\pi\)
\(920\) 13.6136 + 1.55166i 0.448829 + 0.0511567i
\(921\) 10.0258i 0.330362i
\(922\) −23.7286 29.3422i −0.781460 0.966333i
\(923\) −37.7891 37.7891i −1.24384 1.24384i
\(924\) −0.549601 + 2.56889i −0.0180806 + 0.0845104i
\(925\) 33.0873 + 13.2183i 1.08790 + 0.434615i
\(926\) 4.55779 43.0893i 0.149778 1.41600i
\(927\) 45.6952i 1.50083i
\(928\) 4.10633 + 15.5311i 0.134797 + 0.509832i
\(929\) 22.3311 0.732659 0.366330 0.930485i \(-0.380614\pi\)
0.366330 + 0.930485i \(0.380614\pi\)
\(930\) −2.31617 + 2.81711i −0.0759503 + 0.0923768i
\(931\) −0.847544 0.847544i −0.0277771 0.0277771i
\(932\) −34.6677 7.41697i −1.13558 0.242951i
\(933\) 4.76218 + 4.76218i 0.155907 + 0.155907i
\(934\) −13.1751 + 10.6545i −0.431102 + 0.348626i
\(935\) −21.0912 13.9009i −0.689755 0.454607i
\(936\) 12.0749 + 23.8154i 0.394680 + 0.778432i
\(937\) 16.7595 0.547508 0.273754 0.961800i \(-0.411735\pi\)
0.273754 + 0.961800i \(0.411735\pi\)
\(938\) 7.30034 5.90367i 0.238364 0.192762i
\(939\) 3.40288 3.40288i 0.111049 0.111049i
\(940\) 0.268065 33.0740i 0.00874331 1.07875i
\(941\) −6.39091 6.39091i −0.208338 0.208338i 0.595223 0.803561i \(-0.297064\pi\)
−0.803561 + 0.595223i \(0.797064\pi\)
\(942\) 1.11195 10.5124i 0.0362293 0.342511i
\(943\) 23.9469i 0.779817i
\(944\) −29.3694 + 11.1844i −0.955891 + 0.364023i
\(945\) 4.30679 + 2.83854i 0.140100 + 0.0923378i
\(946\) 32.8414 + 3.47381i 1.06776 + 0.112943i
\(947\) 5.70706 5.70706i 0.185454 0.185454i −0.608273 0.793728i \(-0.708138\pi\)
0.793728 + 0.608273i \(0.208138\pi\)
\(948\) −2.02643 + 1.31215i −0.0658152 + 0.0426168i
\(949\) −12.4703 + 12.4703i −0.404802 + 0.404802i
\(950\) 7.49620 + 3.95475i 0.243209 + 0.128309i
\(951\) 7.41028i 0.240295i
\(952\) −2.98519 + 9.12560i −0.0967507 + 0.295762i
\(953\) −34.1804 −1.10721 −0.553606 0.832778i \(-0.686749\pi\)
−0.553606 + 0.832778i \(0.686749\pi\)
\(954\) −7.20590 + 5.82730i −0.233300 + 0.188666i
\(955\) 50.7290 10.4240i 1.64155 0.337312i
\(956\) −16.0443 3.43260i −0.518910 0.111018i
\(957\) −2.63766 + 2.63766i −0.0852634 + 0.0852634i
\(958\) −8.14465 0.861505i −0.263142 0.0278339i
\(959\) −10.8530 −0.350463
\(960\) −6.61865 + 2.45928i −0.213616 + 0.0793729i
\(961\) −22.4627 −0.724602
\(962\) 33.2641 + 3.51853i 1.07248 + 0.113442i
\(963\) 34.5480 34.5480i 1.11329 1.11329i
\(964\) −36.2279 7.75077i −1.16682 0.249635i
\(965\) 4.24406 + 20.6540i 0.136621 + 0.664877i
\(966\) 0.940319 0.760423i 0.0302543 0.0244662i
\(967\) −51.3733 −1.65206 −0.826028 0.563630i \(-0.809405\pi\)
−0.826028 + 0.563630i \(0.809405\pi\)
\(968\) −0.0653069 + 0.199640i −0.00209904 + 0.00641668i
\(969\) 1.60600i 0.0515923i
\(970\) −1.89415 19.4099i −0.0608176 0.623215i
\(971\) 4.56089 4.56089i 0.146366 0.146366i −0.630126 0.776493i \(-0.716997\pi\)
0.776493 + 0.630126i \(0.216997\pi\)
\(972\) 16.6683 10.7931i 0.534637 0.346189i
\(973\) −11.5768 + 11.5768i −0.371137 + 0.371137i
\(974\) 2.05829 + 0.217716i 0.0659518 + 0.00697609i
\(975\) −2.58300 6.01981i −0.0827224 0.192788i
\(976\) 1.08792 + 2.85678i 0.0348235 + 0.0914433i
\(977\) 0.908959i 0.0290802i −0.999894 0.0145401i \(-0.995372\pi\)
0.999894 0.0145401i \(-0.00462842\pi\)
\(978\) −0.250644 + 2.36958i −0.00801470 + 0.0757709i
\(979\) 39.6763 + 39.6763i 1.26806 + 1.26806i
\(980\) 4.47199 + 0.0362455i 0.142852 + 0.00115782i
\(981\) 11.8786 11.8786i 0.379254 0.379254i
\(982\) 3.85313 3.11597i 0.122958 0.0994346i
\(983\) −56.8582 −1.81349 −0.906747 0.421675i \(-0.861442\pi\)
−0.906747 + 0.421675i \(0.861442\pi\)
\(984\) 5.58044 + 11.0064i 0.177898 + 0.350870i
\(985\) −34.0627 22.4502i −1.08533 0.715324i
\(986\) −10.6009 + 8.57278i −0.337601 + 0.273013i
\(987\) −2.06418 2.06418i −0.0657036 0.0657036i
\(988\) 7.78074 + 1.66465i 0.247538 + 0.0529595i
\(989\) −10.7497 10.7497i −0.341821 0.341821i
\(990\) 23.1198 + 19.0086i 0.734795 + 0.604134i
\(991\) −23.9059 −0.759396 −0.379698 0.925111i \(-0.623972\pi\)
−0.379698 + 0.925111i \(0.623972\pi\)
\(992\) 14.2867 + 8.31177i 0.453603 + 0.263899i
\(993\) 6.11570i 0.194076i
\(994\) −2.39516 + 22.6438i −0.0759698 + 0.718217i
\(995\) −2.33763 11.3762i −0.0741078 0.360651i
\(996\) 1.27613 5.96478i 0.0404358 0.189001i
\(997\) 16.0933 + 16.0933i 0.509679 + 0.509679i 0.914428 0.404749i \(-0.132641\pi\)
−0.404749 + 0.914428i \(0.632641\pi\)
\(998\) −33.7930 41.7876i −1.06970 1.32276i
\(999\) 16.4380i 0.520074i
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 560.2.bb.c.29.2 70
5.4 even 2 560.2.bb.d.29.34 yes 70
16.5 even 4 560.2.bb.d.309.34 yes 70
80.69 even 4 inner 560.2.bb.c.309.2 yes 70
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.bb.c.29.2 70 1.1 even 1 trivial
560.2.bb.c.309.2 yes 70 80.69 even 4 inner
560.2.bb.d.29.34 yes 70 5.4 even 2
560.2.bb.d.309.34 yes 70 16.5 even 4