Properties

Label 210.3.v.b.193.2
Level $210$
Weight $3$
Character 210.193
Analytic conductor $5.722$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,3,Mod(37,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.v (of order \(12\), degree \(4\), 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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 193.2
Character \(\chi\) \(=\) 210.193
Dual form 210.3.v.b.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.19534 - 2.72013i) q^{5} -2.44949 q^{6} +(-1.84650 - 6.75207i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.19534 - 2.72013i) q^{5} -2.44949 q^{6} +(-1.84650 - 6.75207i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-4.73531 - 5.25136i) q^{10} +(7.12207 - 12.3358i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(-2.75603 - 2.75603i) q^{13} +(-0.0509352 - 9.89936i) q^{14} +(8.23835 + 2.67014i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-6.41754 - 23.9506i) q^{17} +(4.09808 - 1.09808i) q^{18} +(0.277055 - 0.159958i) q^{19} +(-4.54642 - 8.90674i) q^{20} +(6.11612 + 10.4687i) q^{21} +(14.2441 - 14.2441i) q^{22} +(-3.64915 + 13.6188i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(10.2018 + 22.8237i) q^{25} +(-2.75603 - 4.77358i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.55384 - 13.5414i) q^{28} -24.2642i q^{29} +(10.2765 + 6.66292i) q^{30} +(-7.62013 + 13.1985i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-6.38548 + 23.8309i) q^{33} -35.0661i q^{34} +(-10.6198 + 33.3500i) q^{35} +6.00000 q^{36} +(-2.28156 - 0.611341i) q^{37} +(0.437012 - 0.117097i) q^{38} +(5.84642 + 3.37543i) q^{39} +(-2.95044 - 13.8309i) q^{40} +29.0794 q^{41} +(4.52298 + 16.5391i) q^{42} +(-11.7409 - 11.7409i) q^{43} +(24.6716 - 14.2441i) q^{44} +(-14.9800 - 0.774077i) q^{45} +(-9.96966 + 17.2680i) q^{46} +(-81.7602 - 21.9076i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(-42.1809 + 24.9354i) q^{49} +(5.58190 + 34.9119i) q^{50} +(21.4735 + 37.1932i) q^{51} +(-2.01755 - 7.52961i) q^{52} +(72.6184 - 19.4580i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-63.4344 + 32.3800i) q^{55} +(9.81114 - 17.1971i) q^{56} +(-0.391815 + 0.391815i) q^{57} +(8.88133 - 33.1456i) q^{58} +(31.7156 + 18.3110i) q^{59} +(11.5991 + 12.8632i) q^{60} +(54.2209 + 93.9134i) q^{61} +(-15.2403 + 15.2403i) q^{62} +(-14.9254 - 14.7726i) q^{63} +8.00000i q^{64} +(4.06575 + 19.0592i) q^{65} +(-17.4454 + 30.2164i) q^{66} +(17.6966 + 66.0445i) q^{67} +(12.8351 - 47.9012i) q^{68} -24.4206i q^{69} +(-26.7138 + 41.6698i) q^{70} -20.3365 q^{71} +(8.19615 + 2.19615i) q^{72} +(56.5866 - 15.1623i) q^{73} +(-2.89290 - 1.67022i) q^{74} +(-27.2996 - 33.6115i) q^{75} +0.639831 q^{76} +(-96.4430 - 25.3107i) q^{77} +(6.75087 + 6.75087i) q^{78} +(44.5901 - 25.7441i) q^{79} +(1.03210 - 19.9734i) q^{80} +(4.50000 - 7.79423i) q^{81} +(39.7232 + 10.6438i) q^{82} +(-82.8590 - 82.8590i) q^{83} +(0.124765 + 24.2484i) q^{84} +(-38.2248 + 117.937i) q^{85} +(-11.7409 - 20.3359i) q^{86} +(10.8774 + 40.5949i) q^{87} +(38.9157 - 10.4274i) q^{88} +(95.6273 - 55.2104i) q^{89} +(-20.1797 - 6.54047i) q^{90} +(-13.5199 + 23.6979i) q^{91} +(-19.9393 + 19.9393i) q^{92} +(6.83202 - 25.4975i) q^{93} +(-103.668 - 59.8526i) q^{94} +(-1.59744 - 0.0825463i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(68.2928 - 68.2928i) q^{97} +(-66.7471 + 18.6231i) q^{98} -42.7324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.683013 + 0.183013i
\(3\) −1.67303 + 0.448288i −0.557678 + 0.149429i
\(4\) 1.73205 + 1.00000i 0.433013 + 0.250000i
\(5\) −4.19534 2.72013i −0.839069 0.544025i
\(6\) −2.44949 −0.408248
\(7\) −1.84650 6.75207i −0.263786 0.964581i
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) −4.73531 5.25136i −0.473531 0.525136i
\(11\) 7.12207 12.3358i 0.647461 1.12144i −0.336266 0.941767i \(-0.609164\pi\)
0.983727 0.179669i \(-0.0575025\pi\)
\(12\) −3.34607 0.896575i −0.278839 0.0747146i
\(13\) −2.75603 2.75603i −0.212002 0.212002i 0.593115 0.805118i \(-0.297898\pi\)
−0.805118 + 0.593115i \(0.797898\pi\)
\(14\) −0.0509352 9.89936i −0.00363823 0.707097i
\(15\) 8.23835 + 2.67014i 0.549223 + 0.178009i
\(16\) 2.00000 + 3.46410i 0.125000 + 0.216506i
\(17\) −6.41754 23.9506i −0.377502 1.40886i −0.849654 0.527341i \(-0.823189\pi\)
0.472152 0.881517i \(-0.343477\pi\)
\(18\) 4.09808 1.09808i 0.227671 0.0610042i
\(19\) 0.277055 0.159958i 0.0145818 0.00841882i −0.492691 0.870204i \(-0.663987\pi\)
0.507273 + 0.861785i \(0.330654\pi\)
\(20\) −4.54642 8.90674i −0.227321 0.445337i
\(21\) 6.11612 + 10.4687i 0.291244 + 0.498508i
\(22\) 14.2441 14.2441i 0.647461 0.647461i
\(23\) −3.64915 + 13.6188i −0.158659 + 0.592122i 0.840106 + 0.542423i \(0.182493\pi\)
−0.998764 + 0.0496991i \(0.984174\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 10.2018 + 22.8237i 0.408073 + 0.912949i
\(26\) −2.75603 4.77358i −0.106001 0.183599i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 3.55384 13.5414i 0.126923 0.483622i
\(29\) 24.2642i 0.836698i −0.908286 0.418349i \(-0.862609\pi\)
0.908286 0.418349i \(-0.137391\pi\)
\(30\) 10.2765 + 6.66292i 0.342548 + 0.222097i
\(31\) −7.62013 + 13.1985i −0.245811 + 0.425757i −0.962359 0.271781i \(-0.912387\pi\)
0.716549 + 0.697537i \(0.245721\pi\)
\(32\) 1.46410 + 5.46410i 0.0457532 + 0.170753i
\(33\) −6.38548 + 23.8309i −0.193499 + 0.722149i
\(34\) 35.0661i 1.03136i
\(35\) −10.6198 + 33.3500i −0.303422 + 0.952856i
\(36\) 6.00000 0.166667
\(37\) −2.28156 0.611341i −0.0616637 0.0165227i 0.227855 0.973695i \(-0.426829\pi\)
−0.289519 + 0.957172i \(0.593495\pi\)
\(38\) 0.437012 0.117097i 0.0115003 0.00308150i
\(39\) 5.84642 + 3.37543i 0.149908 + 0.0865496i
\(40\) −2.95044 13.8309i −0.0737610 0.345774i
\(41\) 29.0794 0.709254 0.354627 0.935008i \(-0.384608\pi\)
0.354627 + 0.935008i \(0.384608\pi\)
\(42\) 4.52298 + 16.5391i 0.107690 + 0.393789i
\(43\) −11.7409 11.7409i −0.273045 0.273045i 0.557280 0.830325i \(-0.311845\pi\)
−0.830325 + 0.557280i \(0.811845\pi\)
\(44\) 24.6716 14.2441i 0.560718 0.323731i
\(45\) −14.9800 0.774077i −0.332889 0.0172017i
\(46\) −9.96966 + 17.2680i −0.216732 + 0.375390i
\(47\) −81.7602 21.9076i −1.73958 0.466119i −0.757225 0.653154i \(-0.773445\pi\)
−0.982353 + 0.187035i \(0.940112\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) −42.1809 + 24.9354i −0.860834 + 0.508885i
\(50\) 5.58190 + 34.9119i 0.111638 + 0.698238i
\(51\) 21.4735 + 37.1932i 0.421049 + 0.729279i
\(52\) −2.01755 7.52961i −0.0387991 0.144800i
\(53\) 72.6184 19.4580i 1.37016 0.367133i 0.502622 0.864507i \(-0.332369\pi\)
0.867536 + 0.497374i \(0.165702\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) −63.4344 + 32.3800i −1.15335 + 0.588727i
\(56\) 9.81114 17.1971i 0.175199 0.307092i
\(57\) −0.391815 + 0.391815i −0.00687394 + 0.00687394i
\(58\) 8.88133 33.1456i 0.153126 0.571475i
\(59\) 31.7156 + 18.3110i 0.537553 + 0.310356i 0.744087 0.668083i \(-0.232885\pi\)
−0.206534 + 0.978439i \(0.566218\pi\)
\(60\) 11.5991 + 12.8632i 0.193318 + 0.214386i
\(61\) 54.2209 + 93.9134i 0.888867 + 1.53956i 0.841216 + 0.540699i \(0.181840\pi\)
0.0476513 + 0.998864i \(0.484826\pi\)
\(62\) −15.2403 + 15.2403i −0.245811 + 0.245811i
\(63\) −14.9254 14.7726i −0.236912 0.234486i
\(64\) 8.00000i 0.125000i
\(65\) 4.06575 + 19.0592i 0.0625500 + 0.293219i
\(66\) −17.4454 + 30.2164i −0.264325 + 0.457824i
\(67\) 17.6966 + 66.0445i 0.264128 + 0.985739i 0.962782 + 0.270279i \(0.0871160\pi\)
−0.698654 + 0.715460i \(0.746217\pi\)
\(68\) 12.8351 47.9012i 0.188751 0.704429i
\(69\) 24.4206i 0.353921i
\(70\) −26.7138 + 41.6698i −0.381626 + 0.595283i
\(71\) −20.3365 −0.286429 −0.143215 0.989692i \(-0.545744\pi\)
−0.143215 + 0.989692i \(0.545744\pi\)
\(72\) 8.19615 + 2.19615i 0.113835 + 0.0305021i
\(73\) 56.5866 15.1623i 0.775159 0.207703i 0.150510 0.988609i \(-0.451909\pi\)
0.624649 + 0.780905i \(0.285242\pi\)
\(74\) −2.89290 1.67022i −0.0390932 0.0225705i
\(75\) −27.2996 33.6115i −0.363995 0.448153i
\(76\) 0.639831 0.00841882
\(77\) −96.4430 25.3107i −1.25251 0.328710i
\(78\) 6.75087 + 6.75087i 0.0865496 + 0.0865496i
\(79\) 44.5901 25.7441i 0.564431 0.325874i −0.190491 0.981689i \(-0.561008\pi\)
0.754922 + 0.655815i \(0.227675\pi\)
\(80\) 1.03210 19.9734i 0.0129013 0.249667i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) 39.7232 + 10.6438i 0.484429 + 0.129802i
\(83\) −82.8590 82.8590i −0.998301 0.998301i 0.00169722 0.999999i \(-0.499460\pi\)
−0.999999 + 0.00169722i \(0.999460\pi\)
\(84\) 0.124765 + 24.2484i 0.00148530 + 0.288671i
\(85\) −38.2248 + 117.937i −0.449704 + 1.38750i
\(86\) −11.7409 20.3359i −0.136522 0.236464i
\(87\) 10.8774 + 40.5949i 0.125027 + 0.466608i
\(88\) 38.9157 10.4274i 0.442224 0.118494i
\(89\) 95.6273 55.2104i 1.07446 0.620342i 0.145066 0.989422i \(-0.453660\pi\)
0.929398 + 0.369080i \(0.120327\pi\)
\(90\) −20.1797 6.54047i −0.224219 0.0726719i
\(91\) −13.5199 + 23.6979i −0.148570 + 0.260417i
\(92\) −19.9393 + 19.9393i −0.216732 + 0.216732i
\(93\) 6.83202 25.4975i 0.0734626 0.274166i
\(94\) −103.668 59.8526i −1.10285 0.636730i
\(95\) −1.59744 0.0825463i −0.0168152 0.000868909i
\(96\) −4.89898 8.48528i −0.0510310 0.0883883i
\(97\) 68.2928 68.2928i 0.704050 0.704050i −0.261228 0.965277i \(-0.584127\pi\)
0.965277 + 0.261228i \(0.0841273\pi\)
\(98\) −66.7471 + 18.6231i −0.681093 + 0.190031i
\(99\) 42.7324i 0.431641i
\(100\) −5.15364 + 49.7337i −0.0515364 + 0.497337i
\(101\) 49.9666 86.5447i 0.494719 0.856878i −0.505263 0.862966i \(-0.668604\pi\)
0.999981 + 0.00608738i \(0.00193769\pi\)
\(102\) 15.7197 + 58.6667i 0.154115 + 0.575164i
\(103\) −28.9847 + 108.172i −0.281405 + 1.05022i 0.670022 + 0.742341i \(0.266285\pi\)
−0.951427 + 0.307875i \(0.900382\pi\)
\(104\) 11.0241i 0.106001i
\(105\) 2.81685 60.5563i 0.0268272 0.576727i
\(106\) 106.321 1.00303
\(107\) 107.570 + 28.8233i 1.00533 + 0.269377i 0.723676 0.690140i \(-0.242451\pi\)
0.281652 + 0.959517i \(0.409118\pi\)
\(108\) −10.0382 + 2.68973i −0.0929463 + 0.0249049i
\(109\) 65.8933 + 38.0435i 0.604526 + 0.349023i 0.770820 0.637053i \(-0.219847\pi\)
−0.166294 + 0.986076i \(0.553180\pi\)
\(110\) −98.5050 + 21.0132i −0.895500 + 0.191029i
\(111\) 4.09118 0.0368574
\(112\) 19.6969 19.9006i 0.175865 0.177684i
\(113\) −76.5867 76.5867i −0.677759 0.677759i 0.281734 0.959493i \(-0.409090\pi\)
−0.959493 + 0.281734i \(0.909090\pi\)
\(114\) −0.678643 + 0.391815i −0.00595301 + 0.00343697i
\(115\) 52.3543 47.2094i 0.455255 0.410517i
\(116\) 24.2642 42.0269i 0.209174 0.362301i
\(117\) −11.2944 3.02633i −0.0965335 0.0258661i
\(118\) 36.6220 + 36.6220i 0.310356 + 0.310356i
\(119\) −149.866 + 87.5564i −1.25938 + 0.735768i
\(120\) 11.1364 + 21.8170i 0.0928035 + 0.181808i
\(121\) −40.9478 70.9237i −0.338412 0.586146i
\(122\) 39.6925 + 148.134i 0.325348 + 1.21422i
\(123\) −48.6508 + 13.0359i −0.395535 + 0.105983i
\(124\) −26.3969 + 15.2403i −0.212878 + 0.122905i
\(125\) 19.2832 123.504i 0.154266 0.988029i
\(126\) −14.9814 25.6429i −0.118900 0.203515i
\(127\) −85.3727 + 85.3727i −0.672226 + 0.672226i −0.958229 0.286003i \(-0.907673\pi\)
0.286003 + 0.958229i \(0.407673\pi\)
\(128\) −2.92820 + 10.9282i −0.0228766 + 0.0853766i
\(129\) 24.9063 + 14.3796i 0.193072 + 0.111470i
\(130\) −1.42225 + 27.5236i −0.0109404 + 0.211720i
\(131\) 109.573 + 189.787i 0.836438 + 1.44875i 0.892854 + 0.450347i \(0.148700\pi\)
−0.0564154 + 0.998407i \(0.517967\pi\)
\(132\) −34.8909 + 34.8909i −0.264325 + 0.264325i
\(133\) −1.59163 1.57533i −0.0119671 0.0118446i
\(134\) 96.6959i 0.721611i
\(135\) 25.4091 5.42030i 0.188215 0.0401504i
\(136\) 35.0661 60.7362i 0.257839 0.446590i
\(137\) −53.4994 199.663i −0.390507 1.45739i −0.829300 0.558803i \(-0.811261\pi\)
0.438794 0.898588i \(-0.355406\pi\)
\(138\) 8.93855 33.3591i 0.0647721 0.241733i
\(139\) 217.562i 1.56519i −0.622529 0.782597i \(-0.713895\pi\)
0.622529 0.782597i \(-0.286105\pi\)
\(140\) −51.7440 + 47.1441i −0.369600 + 0.336743i
\(141\) 146.608 1.03978
\(142\) −27.7802 7.44367i −0.195635 0.0524202i
\(143\) −53.6265 + 14.3692i −0.375010 + 0.100484i
\(144\) 10.3923 + 6.00000i 0.0721688 + 0.0416667i
\(145\) −66.0018 + 101.797i −0.455185 + 0.702047i
\(146\) 82.8485 0.567456
\(147\) 59.3918 60.6269i 0.404026 0.412428i
\(148\) −3.34043 3.34043i −0.0225705 0.0225705i
\(149\) 202.765 117.066i 1.36084 0.785680i 0.371102 0.928592i \(-0.378980\pi\)
0.989735 + 0.142913i \(0.0456468\pi\)
\(150\) −24.9893 55.9065i −0.166595 0.372710i
\(151\) −113.664 + 196.871i −0.752739 + 1.30378i 0.193751 + 0.981051i \(0.437935\pi\)
−0.946490 + 0.322732i \(0.895399\pi\)
\(152\) 0.874025 + 0.234194i 0.00575016 + 0.00154075i
\(153\) −52.5991 52.5991i −0.343785 0.343785i
\(154\) −122.479 69.8757i −0.795320 0.453738i
\(155\) 67.8705 34.6443i 0.437874 0.223512i
\(156\) 6.75087 + 11.6928i 0.0432748 + 0.0749541i
\(157\) −27.9400 104.273i −0.177962 0.664162i −0.996028 0.0890386i \(-0.971621\pi\)
0.818066 0.575124i \(-0.195046\pi\)
\(158\) 70.3341 18.8460i 0.445153 0.119278i
\(159\) −112.770 + 65.1078i −0.709246 + 0.409483i
\(160\) 8.72063 26.9063i 0.0545039 0.168165i
\(161\) 98.6933 0.507807i 0.613002 0.00315408i
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) 78.0535 291.300i 0.478856 1.78711i −0.127407 0.991850i \(-0.540666\pi\)
0.606263 0.795264i \(-0.292668\pi\)
\(164\) 50.3670 + 29.0794i 0.307116 + 0.177313i
\(165\) 91.6124 82.6096i 0.555226 0.500664i
\(166\) −82.8590 143.516i −0.499151 0.864554i
\(167\) 55.7819 55.7819i 0.334023 0.334023i −0.520089 0.854112i \(-0.674101\pi\)
0.854112 + 0.520089i \(0.174101\pi\)
\(168\) −8.70509 + 33.1696i −0.0518160 + 0.197438i
\(169\) 153.809i 0.910110i
\(170\) −95.3842 + 147.114i −0.561083 + 0.865378i
\(171\) 0.479873 0.831164i 0.00280627 0.00486061i
\(172\) −8.59496 32.0768i −0.0499707 0.186493i
\(173\) −54.2505 + 202.465i −0.313587 + 1.17032i 0.611712 + 0.791081i \(0.290481\pi\)
−0.925298 + 0.379240i \(0.876185\pi\)
\(174\) 59.4350i 0.341581i
\(175\) 135.270 111.027i 0.772970 0.634443i
\(176\) 56.9766 0.323731
\(177\) −61.2699 16.4172i −0.346158 0.0927526i
\(178\) 150.838 40.4168i 0.847403 0.227061i
\(179\) 130.023 + 75.0691i 0.726388 + 0.419380i 0.817099 0.576497i \(-0.195581\pi\)
−0.0907112 + 0.995877i \(0.528914\pi\)
\(180\) −25.1721 16.3208i −0.139845 0.0906709i
\(181\) 147.164 0.813063 0.406532 0.913637i \(-0.366738\pi\)
0.406532 + 0.913637i \(0.366738\pi\)
\(182\) −27.1426 + 27.4233i −0.149135 + 0.150678i
\(183\) −132.814 132.814i −0.725757 0.725757i
\(184\) −34.5359 + 19.9393i −0.187695 + 0.108366i
\(185\) 7.90899 + 8.77091i 0.0427513 + 0.0474103i
\(186\) 18.6654 32.3295i 0.100352 0.173814i
\(187\) −341.156 91.4124i −1.82436 0.488836i
\(188\) −119.705 119.705i −0.636730 0.636730i
\(189\) 31.5932 + 18.0242i 0.167160 + 0.0953662i
\(190\) −2.15194 0.697466i −0.0113260 0.00367087i
\(191\) −112.126 194.209i −0.587049 1.01680i −0.994617 0.103624i \(-0.966956\pi\)
0.407567 0.913175i \(-0.366377\pi\)
\(192\) −3.58630 13.3843i −0.0186787 0.0697097i
\(193\) 15.7967 4.23272i 0.0818483 0.0219312i −0.217663 0.976024i \(-0.569843\pi\)
0.299511 + 0.954093i \(0.403177\pi\)
\(194\) 118.287 68.2928i 0.609725 0.352025i
\(195\) −15.3462 30.0641i −0.0786982 0.154175i
\(196\) −97.9948 + 1.00845i −0.499974 + 0.00514517i
\(197\) −199.522 + 199.522i −1.01280 + 1.01280i −0.0128826 + 0.999917i \(0.504101\pi\)
−0.999917 + 0.0128826i \(0.995899\pi\)
\(198\) 15.6412 58.3736i 0.0789957 0.294816i
\(199\) 37.1474 + 21.4471i 0.186670 + 0.107774i 0.590423 0.807094i \(-0.298961\pi\)
−0.403753 + 0.914868i \(0.632294\pi\)
\(200\) −25.2438 + 66.0511i −0.126219 + 0.330256i
\(201\) −59.2139 102.561i −0.294596 0.510256i
\(202\) 99.9332 99.9332i 0.494719 0.494719i
\(203\) −163.834 + 44.8039i −0.807063 + 0.220709i
\(204\) 85.8940i 0.421049i
\(205\) −121.998 79.0996i −0.595113 0.385852i
\(206\) −79.1876 + 137.157i −0.384406 + 0.665811i
\(207\) 10.9474 + 40.8564i 0.0528862 + 0.197374i
\(208\) 4.03511 15.0592i 0.0193996 0.0724001i
\(209\) 4.55692i 0.0218034i
\(210\) 26.0130 81.6904i 0.123872 0.389002i
\(211\) 107.346 0.508747 0.254373 0.967106i \(-0.418131\pi\)
0.254373 + 0.967106i \(0.418131\pi\)
\(212\) 145.237 + 38.9161i 0.685079 + 0.183566i
\(213\) 34.0236 9.11660i 0.159735 0.0428009i
\(214\) 136.393 + 78.7467i 0.637352 + 0.367975i
\(215\) 17.3204 + 81.1941i 0.0805602 + 0.377647i
\(216\) −14.6969 −0.0680414
\(217\) 103.187 + 27.0807i 0.475518 + 0.124796i
\(218\) 76.0871 + 76.0871i 0.349023 + 0.349023i
\(219\) −87.8741 + 50.7342i −0.401252 + 0.231663i
\(220\) −142.252 7.35071i −0.646598 0.0334123i
\(221\) −48.3216 + 83.6955i −0.218650 + 0.378712i
\(222\) 5.58865 + 1.49747i 0.0251741 + 0.00674538i
\(223\) 152.586 + 152.586i 0.684241 + 0.684241i 0.960953 0.276712i \(-0.0892448\pi\)
−0.276712 + 0.960953i \(0.589245\pi\)
\(224\) 34.1905 19.9752i 0.152636 0.0891749i
\(225\) 60.7407 + 43.9950i 0.269959 + 0.195533i
\(226\) −76.5867 132.652i −0.338879 0.586956i
\(227\) 83.4520 + 311.447i 0.367630 + 1.37201i 0.863820 + 0.503800i \(0.168065\pi\)
−0.496190 + 0.868214i \(0.665268\pi\)
\(228\) −1.07046 + 0.286828i −0.00469499 + 0.00125802i
\(229\) −80.3357 + 46.3818i −0.350811 + 0.202541i −0.665042 0.746806i \(-0.731587\pi\)
0.314232 + 0.949346i \(0.398253\pi\)
\(230\) 88.7971 45.3263i 0.386075 0.197071i
\(231\) 172.699 0.888587i 0.747614 0.00384670i
\(232\) 48.5285 48.5285i 0.209174 0.209174i
\(233\) −98.3603 + 367.086i −0.422147 + 1.57547i 0.347928 + 0.937521i \(0.386885\pi\)
−0.770075 + 0.637953i \(0.779781\pi\)
\(234\) −14.3208 8.26809i −0.0611998 0.0353337i
\(235\) 283.421 + 314.308i 1.20605 + 1.33748i
\(236\) 36.6220 + 63.4312i 0.155178 + 0.268776i
\(237\) −63.0599 + 63.0599i −0.266075 + 0.266075i
\(238\) −236.769 + 64.7495i −0.994826 + 0.272057i
\(239\) 196.297i 0.821327i 0.911787 + 0.410664i \(0.134703\pi\)
−0.911787 + 0.410664i \(0.865297\pi\)
\(240\) 7.22707 + 33.8787i 0.0301128 + 0.141161i
\(241\) −188.179 + 325.936i −0.780826 + 1.35243i 0.150635 + 0.988589i \(0.451868\pi\)
−0.931461 + 0.363841i \(0.881465\pi\)
\(242\) −29.9759 111.872i −0.123867 0.462279i
\(243\) −4.03459 + 15.0573i −0.0166032 + 0.0619642i
\(244\) 216.884i 0.888867i
\(245\) 244.791 + 10.1248i 0.999146 + 0.0413258i
\(246\) −71.2297 −0.289552
\(247\) −1.20442 0.322723i −0.00487619 0.00130657i
\(248\) −41.6372 + 11.1566i −0.167892 + 0.0449865i
\(249\) 175.771 + 101.481i 0.705906 + 0.407555i
\(250\) 71.5468 161.651i 0.286187 0.646604i
\(251\) −193.073 −0.769215 −0.384607 0.923080i \(-0.625663\pi\)
−0.384607 + 0.923080i \(0.625663\pi\)
\(252\) −11.0790 40.5124i −0.0439643 0.160764i
\(253\) 142.009 + 142.009i 0.561301 + 0.561301i
\(254\) −147.870 + 85.3727i −0.582164 + 0.336113i
\(255\) 11.0814 214.449i 0.0434566 0.840976i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 208.500 + 55.8673i 0.811283 + 0.217383i 0.640532 0.767932i \(-0.278714\pi\)
0.170751 + 0.985314i \(0.445381\pi\)
\(258\) 28.7593 + 28.7593i 0.111470 + 0.111470i
\(259\) 0.0850728 + 16.5341i 0.000328466 + 0.0638381i
\(260\) −12.0172 + 37.0773i −0.0462198 + 0.142605i
\(261\) −36.3964 63.0403i −0.139450 0.241534i
\(262\) 80.2133 + 299.360i 0.306158 + 1.14260i
\(263\) −433.000 + 116.022i −1.64639 + 0.441148i −0.958599 0.284761i \(-0.908086\pi\)
−0.687790 + 0.725910i \(0.741419\pi\)
\(264\) −60.4328 + 34.8909i −0.228912 + 0.132162i
\(265\) −357.587 115.898i −1.34939 0.437351i
\(266\) −1.59759 2.73452i −0.00600598 0.0102801i
\(267\) −135.237 + 135.237i −0.506507 + 0.506507i
\(268\) −35.3931 + 132.089i −0.132064 + 0.492869i
\(269\) 93.0558 + 53.7258i 0.345932 + 0.199724i 0.662892 0.748715i \(-0.269329\pi\)
−0.316960 + 0.948439i \(0.602662\pi\)
\(270\) 36.6934 + 1.89609i 0.135901 + 0.00702257i
\(271\) −98.0395 169.809i −0.361769 0.626603i 0.626483 0.779435i \(-0.284494\pi\)
−0.988252 + 0.152833i \(0.951160\pi\)
\(272\) 70.1322 70.1322i 0.257839 0.257839i
\(273\) 11.9957 45.7082i 0.0439405 0.167429i
\(274\) 292.326i 1.06688i
\(275\) 354.207 + 36.7046i 1.28803 + 0.133471i
\(276\) 24.4206 42.2977i 0.0884803 0.153252i
\(277\) −96.4285 359.876i −0.348117 1.29919i −0.888928 0.458048i \(-0.848549\pi\)
0.540810 0.841145i \(-0.318118\pi\)
\(278\) 79.6332 297.195i 0.286450 1.06905i
\(279\) 45.7208i 0.163874i
\(280\) −87.9395 + 45.4604i −0.314070 + 0.162358i
\(281\) −256.628 −0.913268 −0.456634 0.889655i \(-0.650945\pi\)
−0.456634 + 0.889655i \(0.650945\pi\)
\(282\) 200.271 + 53.6624i 0.710180 + 0.190292i
\(283\) 401.426 107.562i 1.41846 0.380076i 0.533526 0.845784i \(-0.320867\pi\)
0.884939 + 0.465707i \(0.154200\pi\)
\(284\) −35.2238 20.3365i −0.124028 0.0716074i
\(285\) 2.70958 0.578012i 0.00950731 0.00202811i
\(286\) −78.5146 −0.274526
\(287\) −53.6951 196.346i −0.187091 0.684133i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) −282.164 + 162.908i −0.976347 + 0.563694i
\(290\) −127.420 + 114.899i −0.439380 + 0.396203i
\(291\) −83.6413 + 144.871i −0.287427 + 0.497838i
\(292\) 113.173 + 30.3247i 0.387579 + 0.103852i
\(293\) 236.224 + 236.224i 0.806226 + 0.806226i 0.984060 0.177834i \(-0.0569091\pi\)
−0.177834 + 0.984060i \(0.556909\pi\)
\(294\) 103.322 61.0789i 0.351434 0.207752i
\(295\) −83.2497 163.092i −0.282202 0.552853i
\(296\) −3.34043 5.78580i −0.0112852 0.0195466i
\(297\) 19.1564 + 71.4928i 0.0644998 + 0.240716i
\(298\) 319.831 85.6984i 1.07326 0.287579i
\(299\) 47.5910 27.4767i 0.159167 0.0918952i
\(300\) −13.6728 85.5164i −0.0455760 0.285055i
\(301\) −57.5960 + 100.955i −0.191349 + 0.335399i
\(302\) −227.327 + 227.327i −0.752739 + 0.752739i
\(303\) −44.7988 + 167.192i −0.147851 + 0.551787i
\(304\) 1.10822 + 0.639831i 0.00364546 + 0.00210471i
\(305\) 27.9808 541.487i 0.0917402 1.77537i
\(306\) −52.5991 91.1044i −0.171893 0.297727i
\(307\) −106.527 + 106.527i −0.346995 + 0.346995i −0.858989 0.511994i \(-0.828907\pi\)
0.511994 + 0.858989i \(0.328907\pi\)
\(308\) −141.733 140.282i −0.460174 0.455462i
\(309\) 193.969i 0.627732i
\(310\) 105.394 22.4827i 0.339979 0.0725249i
\(311\) −102.511 + 177.554i −0.329617 + 0.570914i −0.982436 0.186601i \(-0.940253\pi\)
0.652819 + 0.757514i \(0.273586\pi\)
\(312\) 4.94198 + 18.4437i 0.0158397 + 0.0591145i
\(313\) −62.5250 + 233.347i −0.199760 + 0.745516i 0.791223 + 0.611528i \(0.209445\pi\)
−0.990983 + 0.133988i \(0.957222\pi\)
\(314\) 152.667i 0.486201i
\(315\) 22.4340 + 102.575i 0.0712189 + 0.325636i
\(316\) 102.976 0.325874
\(317\) 225.154 + 60.3297i 0.710263 + 0.190315i 0.595823 0.803116i \(-0.296826\pi\)
0.114440 + 0.993430i \(0.463493\pi\)
\(318\) −177.878 + 47.6623i −0.559365 + 0.149881i
\(319\) −299.319 172.812i −0.938303 0.541729i
\(320\) 21.7610 33.5628i 0.0680031 0.104884i
\(321\) −192.889 −0.600901
\(322\) 135.003 + 35.4306i 0.419265 + 0.110033i
\(323\) −5.60909 5.60909i −0.0173656 0.0173656i
\(324\) 15.5885 9.00000i 0.0481125 0.0277778i
\(325\) 34.7863 91.0194i 0.107035 0.280060i
\(326\) 213.246 369.353i 0.654129 1.13299i
\(327\) −127.296 34.1089i −0.389285 0.104309i
\(328\) 58.1588 + 58.1588i 0.177313 + 0.177313i
\(329\) 3.04861 + 592.503i 0.00926628 + 1.80092i
\(330\) 155.382 79.3144i 0.470855 0.240347i
\(331\) −182.812 316.640i −0.552303 0.956617i −0.998108 0.0614865i \(-0.980416\pi\)
0.445805 0.895130i \(-0.352917\pi\)
\(332\) −60.6570 226.375i −0.182702 0.681852i
\(333\) −6.84467 + 1.83402i −0.0205546 + 0.00550758i
\(334\) 96.6171 55.7819i 0.289273 0.167012i
\(335\) 105.406 325.216i 0.314645 0.970795i
\(336\) −24.0323 + 42.1242i −0.0715247 + 0.125370i
\(337\) 392.860 392.860i 1.16576 1.16576i 0.182562 0.983194i \(-0.441561\pi\)
0.983194 0.182562i \(-0.0584389\pi\)
\(338\) 56.2979 210.106i 0.166562 0.621617i
\(339\) 162.465 + 93.7992i 0.479248 + 0.276694i
\(340\) −184.145 + 166.049i −0.541602 + 0.488379i
\(341\) 108.542 + 188.001i 0.318306 + 0.551322i
\(342\) 0.959746 0.959746i 0.00280627 0.00280627i
\(343\) 246.252 + 238.765i 0.717937 + 0.696108i
\(344\) 46.9637i 0.136522i
\(345\) −66.4270 + 102.453i −0.192542 + 0.296964i
\(346\) −148.215 + 256.716i −0.428367 + 0.741954i
\(347\) −73.5268 274.406i −0.211893 0.790795i −0.987237 0.159256i \(-0.949090\pi\)
0.775344 0.631539i \(-0.217576\pi\)
\(348\) −21.7547 + 81.1897i −0.0625136 + 0.233304i
\(349\) 345.311i 0.989429i −0.869055 0.494715i \(-0.835273\pi\)
0.869055 0.494715i \(-0.164727\pi\)
\(350\) 225.421 102.154i 0.644059 0.291869i
\(351\) 20.2526 0.0576997
\(352\) 77.8315 + 20.8549i 0.221112 + 0.0592468i
\(353\) 570.810 152.948i 1.61703 0.433281i 0.666900 0.745148i \(-0.267621\pi\)
0.950126 + 0.311867i \(0.100954\pi\)
\(354\) −77.6871 44.8527i −0.219455 0.126702i
\(355\) 85.3186 + 55.3178i 0.240334 + 0.155825i
\(356\) 220.842 0.620342
\(357\) 211.480 213.668i 0.592382 0.598509i
\(358\) 150.138 + 150.138i 0.419380 + 0.419380i
\(359\) −358.501 + 206.981i −0.998611 + 0.576549i −0.907837 0.419323i \(-0.862267\pi\)
−0.0907742 + 0.995871i \(0.528934\pi\)
\(360\) −28.4119 31.5082i −0.0789219 0.0875227i
\(361\) −180.449 + 312.547i −0.499858 + 0.865780i
\(362\) 201.030 + 53.8659i 0.555332 + 0.148801i
\(363\) 100.301 + 100.301i 0.276312 + 0.276312i
\(364\) −47.1151 + 27.5261i −0.129437 + 0.0756211i
\(365\) −278.644 90.3115i −0.763408 0.247429i
\(366\) −132.814 230.040i −0.362879 0.628524i
\(367\) −110.300 411.646i −0.300545 1.12165i −0.936713 0.350099i \(-0.886148\pi\)
0.636167 0.771551i \(-0.280519\pi\)
\(368\) −54.4752 + 14.5966i −0.148030 + 0.0396647i
\(369\) 75.5505 43.6191i 0.204744 0.118209i
\(370\) 7.59351 + 14.8762i 0.0205230 + 0.0402059i
\(371\) −265.472 454.395i −0.715557 1.22478i
\(372\) 37.3309 37.3309i 0.100352 0.100352i
\(373\) −41.7458 + 155.797i −0.111919 + 0.417687i −0.999038 0.0438534i \(-0.986037\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(374\) −432.568 249.743i −1.15660 0.667763i
\(375\) 23.1038 + 215.270i 0.0616100 + 0.574054i
\(376\) −119.705 207.336i −0.318365 0.551424i
\(377\) −66.8730 + 66.8730i −0.177382 + 0.177382i
\(378\) 36.5597 + 36.1854i 0.0967189 + 0.0957287i
\(379\) 230.272i 0.607577i 0.952740 + 0.303788i \(0.0982516\pi\)
−0.952740 + 0.303788i \(0.901748\pi\)
\(380\) −2.68431 1.74042i −0.00706397 0.00458005i
\(381\) 104.560 181.103i 0.274435 0.475335i
\(382\) −82.0822 306.335i −0.214875 0.801924i
\(383\) 37.6089 140.358i 0.0981956 0.366471i −0.899289 0.437355i \(-0.855915\pi\)
0.997485 + 0.0708839i \(0.0225820\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 335.763 + 368.524i 0.872113 + 0.957206i
\(386\) 23.1280 0.0599171
\(387\) −48.1152 12.8924i −0.124329 0.0333138i
\(388\) 186.579 49.9938i 0.480875 0.128850i
\(389\) −414.884 239.533i −1.06654 0.615767i −0.139306 0.990249i \(-0.544487\pi\)
−0.927234 + 0.374483i \(0.877820\pi\)
\(390\) −9.95901 46.6854i −0.0255359 0.119706i
\(391\) 349.597 0.894110
\(392\) −134.233 34.4910i −0.342430 0.0879873i
\(393\) −268.399 268.399i −0.682949 0.682949i
\(394\) −345.581 + 199.522i −0.877110 + 0.506400i
\(395\) −257.098 13.2853i −0.650880 0.0336336i
\(396\) 42.7324 74.0147i 0.107910 0.186906i
\(397\) 8.52545 + 2.28439i 0.0214747 + 0.00575412i 0.269540 0.962989i \(-0.413128\pi\)
−0.248066 + 0.968743i \(0.579795\pi\)
\(398\) 42.8941 + 42.8941i 0.107774 + 0.107774i
\(399\) 3.36904 + 1.92207i 0.00844372 + 0.00481723i
\(400\) −58.6600 + 80.9876i −0.146650 + 0.202469i
\(401\) −396.991 687.608i −0.990002 1.71473i −0.617155 0.786841i \(-0.711715\pi\)
−0.372847 0.927893i \(-0.621618\pi\)
\(402\) −43.3476 161.775i −0.107830 0.402426i
\(403\) 57.3766 15.3740i 0.142374 0.0381489i
\(404\) 173.089 99.9332i 0.428439 0.247359i
\(405\) −40.0803 + 20.4589i −0.0989638 + 0.0505158i
\(406\) −240.201 + 1.23590i −0.591627 + 0.00304410i
\(407\) −23.7908 + 23.7908i −0.0584540 + 0.0584540i
\(408\) −31.4394 + 117.333i −0.0770573 + 0.287582i
\(409\) −521.846 301.288i −1.27591 0.736645i −0.299814 0.953998i \(-0.596925\pi\)
−0.976093 + 0.217352i \(0.930258\pi\)
\(410\) −137.700 152.707i −0.335854 0.372455i
\(411\) 179.013 + 310.059i 0.435554 + 0.754401i
\(412\) −158.375 + 158.375i −0.384406 + 0.384406i
\(413\) 65.0744 247.957i 0.157565 0.600381i
\(414\) 59.8179i 0.144488i
\(415\) 122.235 + 573.009i 0.294543 + 1.38074i
\(416\) 11.0241 19.0943i 0.0265003 0.0458998i
\(417\) 97.5303 + 363.988i 0.233886 + 0.872873i
\(418\) 1.66795 6.22487i 0.00399031 0.0148920i
\(419\) 341.414i 0.814831i 0.913243 + 0.407415i \(0.133570\pi\)
−0.913243 + 0.407415i \(0.866430\pi\)
\(420\) 65.4352 102.070i 0.155798 0.243023i
\(421\) 94.3393 0.224084 0.112042 0.993703i \(-0.464261\pi\)
0.112042 + 0.993703i \(0.464261\pi\)
\(422\) 146.637 + 39.2912i 0.347481 + 0.0931071i
\(423\) −245.281 + 65.7227i −0.579859 + 0.155373i
\(424\) 184.153 + 106.321i 0.434323 + 0.250756i
\(425\) 481.171 390.812i 1.13217 0.919558i
\(426\) 49.8140 0.116934
\(427\) 533.991 539.514i 1.25056 1.26350i
\(428\) 157.493 + 157.493i 0.367975 + 0.367975i
\(429\) 83.2773 48.0802i 0.194120 0.112075i
\(430\) −6.05892 + 117.253i −0.0140905 + 0.272681i
\(431\) 149.099 258.247i 0.345937 0.599181i −0.639586 0.768719i \(-0.720894\pi\)
0.985524 + 0.169538i \(0.0542276\pi\)
\(432\) −20.0764 5.37945i −0.0464731 0.0124524i
\(433\) 466.639 + 466.639i 1.07769 + 1.07769i 0.996716 + 0.0809720i \(0.0258024\pi\)
0.0809720 + 0.996716i \(0.474198\pi\)
\(434\) 131.044 + 74.7622i 0.301946 + 0.172263i
\(435\) 64.7889 199.897i 0.148940 0.459534i
\(436\) 76.0871 + 131.787i 0.174512 + 0.302263i
\(437\) 1.16742 + 4.35686i 0.00267144 + 0.00996994i
\(438\) −138.608 + 37.1400i −0.316457 + 0.0847945i
\(439\) 66.2436 38.2457i 0.150897 0.0871201i −0.422651 0.906293i \(-0.638900\pi\)
0.573547 + 0.819173i \(0.305567\pi\)
\(440\) −191.629 62.1090i −0.435520 0.141157i
\(441\) −72.1861 + 128.055i −0.163687 + 0.290375i
\(442\) −96.6432 + 96.6432i −0.218650 + 0.218650i
\(443\) 54.6666 204.019i 0.123401 0.460538i −0.876377 0.481626i \(-0.840046\pi\)
0.999778 + 0.0210878i \(0.00671296\pi\)
\(444\) 7.08612 + 4.09118i 0.0159597 + 0.00921436i
\(445\) −551.369 28.4914i −1.23903 0.0640256i
\(446\) 152.586 + 264.286i 0.342120 + 0.592570i
\(447\) −286.753 + 286.753i −0.641505 + 0.641505i
\(448\) 54.0166 14.7720i 0.120573 0.0329732i
\(449\) 400.930i 0.892940i −0.894799 0.446470i \(-0.852681\pi\)
0.894799 0.446470i \(-0.147319\pi\)
\(450\) 66.8701 + 82.3310i 0.148600 + 0.182958i
\(451\) 207.106 358.718i 0.459214 0.795383i
\(452\) −56.0654 209.239i −0.124038 0.462918i
\(453\) 101.908 380.326i 0.224963 0.839572i
\(454\) 455.990i 1.00438i
\(455\) 121.182 62.6451i 0.266334 0.137681i
\(456\) −1.56726 −0.00343697
\(457\) 707.134 + 189.476i 1.54734 + 0.414608i 0.928629 0.371011i \(-0.120989\pi\)
0.618711 + 0.785619i \(0.287655\pi\)
\(458\) −126.717 + 33.9538i −0.276676 + 0.0741350i
\(459\) 111.580 + 64.4205i 0.243093 + 0.140350i
\(460\) 137.890 29.4149i 0.299760 0.0639453i
\(461\) −457.122 −0.991589 −0.495794 0.868440i \(-0.665123\pi\)
−0.495794 + 0.868440i \(0.665123\pi\)
\(462\) 236.236 + 61.9983i 0.511334 + 0.134195i
\(463\) −409.466 409.466i −0.884376 0.884376i 0.109600 0.993976i \(-0.465043\pi\)
−0.993976 + 0.109600i \(0.965043\pi\)
\(464\) 84.0538 48.5285i 0.181150 0.104587i
\(465\) −98.0190 + 88.3867i −0.210793 + 0.190079i
\(466\) −268.725 + 465.446i −0.576664 + 0.998811i
\(467\) 140.174 + 37.5596i 0.300159 + 0.0804275i 0.405756 0.913982i \(-0.367008\pi\)
−0.105596 + 0.994409i \(0.533675\pi\)
\(468\) −16.5362 16.5362i −0.0353337 0.0353337i
\(469\) 413.260 241.440i 0.881152 0.514796i
\(470\) 272.115 + 533.092i 0.578969 + 1.13424i
\(471\) 93.4891 + 161.928i 0.198491 + 0.343796i
\(472\) 26.8092 + 100.053i 0.0567992 + 0.211977i
\(473\) −228.453 + 61.2139i −0.482988 + 0.129416i
\(474\) −109.223 + 63.0599i −0.230428 + 0.133038i
\(475\) 6.47730 + 4.69156i 0.0136364 + 0.00987697i
\(476\) −347.132 + 1.78610i −0.729269 + 0.00375231i
\(477\) 159.481 159.481i 0.334342 0.334342i
\(478\) −71.8498 + 268.147i −0.150313 + 0.560977i
\(479\) 128.423 + 74.1449i 0.268106 + 0.154791i 0.628027 0.778192i \(-0.283863\pi\)
−0.359921 + 0.932983i \(0.617196\pi\)
\(480\) −2.52812 + 48.9245i −0.00526692 + 0.101926i
\(481\) 4.60316 + 7.97291i 0.00956999 + 0.0165757i
\(482\) −376.358 + 376.358i −0.780826 + 0.780826i
\(483\) −164.889 + 45.0926i −0.341386 + 0.0933593i
\(484\) 163.791i 0.338412i
\(485\) −472.277 + 100.747i −0.973767 + 0.207725i
\(486\) −11.0227 + 19.0919i −0.0226805 + 0.0392837i
\(487\) 86.4990 + 322.819i 0.177616 + 0.662872i 0.996091 + 0.0883300i \(0.0281530\pi\)
−0.818475 + 0.574542i \(0.805180\pi\)
\(488\) −79.3849 + 296.269i −0.162674 + 0.607108i
\(489\) 522.344i 1.06819i
\(490\) 330.684 + 103.430i 0.674866 + 0.211082i
\(491\) 241.966 0.492801 0.246401 0.969168i \(-0.420752\pi\)
0.246401 + 0.969168i \(0.420752\pi\)
\(492\) −97.3016 26.0719i −0.197767 0.0529916i
\(493\) −581.143 + 155.717i −1.17879 + 0.315855i
\(494\) −1.52714 0.881696i −0.00309138 0.00178481i
\(495\) −116.238 + 179.277i −0.234823 + 0.362176i
\(496\) −60.9610 −0.122905
\(497\) 37.5513 + 137.313i 0.0755559 + 0.276284i
\(498\) 202.962 + 202.962i 0.407555 + 0.407555i
\(499\) 578.512 334.004i 1.15934 0.669346i 0.208196 0.978087i \(-0.433241\pi\)
0.951146 + 0.308741i \(0.0999076\pi\)
\(500\) 156.903 194.631i 0.313806 0.389263i
\(501\) −68.3186 + 118.331i −0.136364 + 0.236190i
\(502\) −263.742 70.6696i −0.525383 0.140776i
\(503\) 457.165 + 457.165i 0.908876 + 0.908876i 0.996182 0.0873055i \(-0.0278256\pi\)
−0.0873055 + 0.996182i \(0.527826\pi\)
\(504\) −0.305611 59.3962i −0.000606372 0.117850i
\(505\) −445.040 + 227.169i −0.881267 + 0.449840i
\(506\) 142.009 + 245.967i 0.280651 + 0.486101i
\(507\) 68.9505 + 257.327i 0.135997 + 0.507548i
\(508\) −233.242 + 62.4971i −0.459139 + 0.123026i
\(509\) 438.332 253.071i 0.861164 0.497193i −0.00323811 0.999995i \(-0.501031\pi\)
0.864402 + 0.502802i \(0.167697\pi\)
\(510\) 93.6313 288.887i 0.183591 0.566444i
\(511\) −206.864 354.079i −0.404822 0.692915i
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) −0.430242 + 1.60569i −0.000838679 + 0.00312999i
\(514\) 264.367 + 152.632i 0.514333 + 0.296950i
\(515\) 415.843 374.978i 0.807462 0.728113i
\(516\) 28.7593 + 49.8125i 0.0557351 + 0.0965359i
\(517\) −852.549 + 852.549i −1.64903 + 1.64903i
\(518\) −5.93568 + 22.6171i −0.0114588 + 0.0436624i
\(519\) 363.051i 0.699521i
\(520\) −29.9870 + 46.2500i −0.0576673 + 0.0889423i
\(521\) 63.4901 109.968i 0.121862 0.211071i −0.798640 0.601809i \(-0.794447\pi\)
0.920502 + 0.390738i \(0.127780\pi\)
\(522\) −26.6440 99.4367i −0.0510421 0.190492i
\(523\) 99.9181 372.899i 0.191048 0.713001i −0.802207 0.597046i \(-0.796341\pi\)
0.993255 0.115954i \(-0.0369925\pi\)
\(524\) 438.294i 0.836438i
\(525\) −176.538 + 246.392i −0.336264 + 0.469319i
\(526\) −633.956 −1.20524
\(527\) 365.013 + 97.8050i 0.692625 + 0.185588i
\(528\) −95.3237 + 25.5419i −0.180537 + 0.0483748i
\(529\) 285.972 + 165.106i 0.540590 + 0.312110i
\(530\) −446.052 289.206i −0.841607 0.545671i
\(531\) 109.866 0.206904
\(532\) −1.18145 4.32018i −0.00222076 0.00812064i
\(533\) −80.1437 80.1437i −0.150363 0.150363i
\(534\) −234.238 + 135.237i −0.438648 + 0.253254i
\(535\) −372.890 413.528i −0.696991 0.772949i
\(536\) −96.6959 + 167.482i −0.180403 + 0.312467i
\(537\) −251.186 67.3051i −0.467758 0.125335i
\(538\) 107.452 + 107.452i 0.199724 + 0.199724i
\(539\) 7.18227 + 697.926i 0.0133252 + 1.29485i
\(540\) 49.4301 + 16.0208i 0.0915372 + 0.0296682i
\(541\) −85.0505 147.312i −0.157210 0.272295i 0.776652 0.629930i \(-0.216917\pi\)
−0.933861 + 0.357635i \(0.883583\pi\)
\(542\) −71.7699 267.849i −0.132417 0.494186i
\(543\) −246.211 + 65.9720i −0.453427 + 0.121495i
\(544\) 121.472 70.1322i 0.223295 0.128919i
\(545\) −172.962 338.844i −0.317362 0.621732i
\(546\) 33.1169 58.0478i 0.0606536 0.106315i
\(547\) 6.88719 6.88719i 0.0125908 0.0125908i −0.700783 0.713374i \(-0.747166\pi\)
0.713374 + 0.700783i \(0.247166\pi\)
\(548\) 106.999 399.325i 0.195253 0.728695i
\(549\) 281.740 + 162.663i 0.513188 + 0.296289i
\(550\) 470.421 + 179.788i 0.855311 + 0.326887i
\(551\) −3.88125 6.72252i −0.00704401 0.0122006i
\(552\) 48.8411 48.8411i 0.0884803 0.0884803i
\(553\) −256.161 253.539i −0.463221 0.458479i
\(554\) 526.895i 0.951075i
\(555\) −17.1639 11.1285i −0.0309259 0.0200514i
\(556\) 217.562 376.828i 0.391298 0.677749i
\(557\) 59.4417 + 221.839i 0.106718 + 0.398276i 0.998534 0.0541213i \(-0.0172358\pi\)
−0.891817 + 0.452397i \(0.850569\pi\)
\(558\) −16.7350 + 62.4558i −0.0299910 + 0.111928i
\(559\) 64.7167i 0.115772i
\(560\) −136.767 + 29.9119i −0.244227 + 0.0534142i
\(561\) 611.743 1.09045
\(562\) −350.561 93.9325i −0.623774 0.167140i
\(563\) 355.000 95.1221i 0.630551 0.168956i 0.0706314 0.997502i \(-0.477499\pi\)
0.559920 + 0.828547i \(0.310832\pi\)
\(564\) 253.933 + 146.608i 0.450236 + 0.259944i
\(565\) 112.982 + 529.633i 0.199968 + 0.937404i
\(566\) 587.728 1.03839
\(567\) −60.9364 15.9923i −0.107472 0.0282051i
\(568\) −40.6730 40.6730i −0.0716074 0.0716074i
\(569\) −528.553 + 305.160i −0.928916 + 0.536310i −0.886468 0.462789i \(-0.846849\pi\)
−0.0424473 + 0.999099i \(0.513515\pi\)
\(570\) 3.91293 + 0.202196i 0.00686478 + 0.000354730i
\(571\) −52.9782 + 91.7610i −0.0927815 + 0.160702i −0.908681 0.417492i \(-0.862909\pi\)
0.815899 + 0.578194i \(0.196242\pi\)
\(572\) −107.253 28.7383i −0.187505 0.0502418i
\(573\) 274.653 + 274.653i 0.479324 + 0.479324i
\(574\) −1.48117 287.868i −0.00258043 0.501512i
\(575\) −348.060 + 55.6496i −0.605322 + 0.0967819i
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −21.3154 79.5502i −0.0369418 0.137869i 0.944992 0.327093i \(-0.106069\pi\)
−0.981934 + 0.189225i \(0.939403\pi\)
\(578\) −445.072 + 119.257i −0.770021 + 0.206326i
\(579\) −24.5309 + 14.1629i −0.0423678 + 0.0244610i
\(580\) −216.115 + 110.316i −0.372613 + 0.190199i
\(581\) −406.471 + 712.469i −0.699605 + 1.22628i
\(582\) −167.283 + 167.283i −0.287427 + 0.287427i
\(583\) 277.163 1034.39i 0.475408 1.77425i
\(584\) 143.498 + 82.8485i 0.245716 + 0.141864i
\(585\) 39.1520 + 43.4187i 0.0669265 + 0.0742201i
\(586\) 236.224 + 409.153i 0.403113 + 0.698212i
\(587\) 81.9493 81.9493i 0.139607 0.139607i −0.633849 0.773456i \(-0.718526\pi\)
0.773456 + 0.633849i \(0.218526\pi\)
\(588\) 163.496 45.6170i 0.278055 0.0775800i
\(589\) 4.87559i 0.00827775i
\(590\) −54.0255 253.259i −0.0915687 0.429252i
\(591\) 244.363 423.249i 0.413474 0.716157i
\(592\) −2.44537 9.12623i −0.00413068 0.0154159i
\(593\) −104.733 + 390.869i −0.176616 + 0.659139i 0.819655 + 0.572857i \(0.194165\pi\)
−0.996271 + 0.0862815i \(0.972502\pi\)
\(594\) 104.673i 0.176217i
\(595\) 866.904 + 40.3252i 1.45698 + 0.0677734i
\(596\) 468.265 0.785680
\(597\) −71.7633 19.2289i −0.120206 0.0322092i
\(598\) 75.0677 20.1143i 0.125531 0.0336360i
\(599\) −688.462 397.484i −1.14935 0.663579i −0.200623 0.979669i \(-0.564297\pi\)
−0.948729 + 0.316090i \(0.897630\pi\)
\(600\) 12.6238 121.822i 0.0210396 0.203037i
\(601\) −225.975 −0.375999 −0.187999 0.982169i \(-0.560200\pi\)
−0.187999 + 0.982169i \(0.560200\pi\)
\(602\) −115.630 + 116.826i −0.192076 + 0.194063i
\(603\) 145.044 + 145.044i 0.240537 + 0.240537i
\(604\) −393.742 + 227.327i −0.651891 + 0.376370i
\(605\) −21.1312 + 408.933i −0.0349276 + 0.675922i
\(606\) −122.393 + 211.990i −0.201968 + 0.349819i
\(607\) −769.756 206.256i −1.26813 0.339795i −0.438817 0.898576i \(-0.644602\pi\)
−0.829315 + 0.558781i \(0.811269\pi\)
\(608\) 1.27966 + 1.27966i 0.00210471 + 0.00210471i
\(609\) 254.014 148.403i 0.417101 0.243683i
\(610\) 236.420 729.443i 0.387574 1.19581i
\(611\) 164.956 + 285.711i 0.269976 + 0.467613i
\(612\) −38.5052 143.704i −0.0629171 0.234810i
\(613\) −283.367 + 75.9279i −0.462262 + 0.123863i −0.482431 0.875934i \(-0.660246\pi\)
0.0201690 + 0.999797i \(0.493580\pi\)
\(614\) −184.511 + 106.527i −0.300506 + 0.173497i
\(615\) 239.566 + 77.6460i 0.389539 + 0.126254i
\(616\) −142.265 243.507i −0.230949 0.395304i
\(617\) −20.6583 + 20.6583i −0.0334818 + 0.0334818i −0.723649 0.690168i \(-0.757537\pi\)
0.690168 + 0.723649i \(0.257537\pi\)
\(618\) 70.9977 264.967i 0.114883 0.428749i
\(619\) −61.3713 35.4327i −0.0991458 0.0572419i 0.449607 0.893226i \(-0.351564\pi\)
−0.548753 + 0.835984i \(0.684897\pi\)
\(620\) 152.200 + 7.86475i 0.245483 + 0.0126851i
\(621\) −36.6309 63.4465i −0.0589869 0.102168i
\(622\) −205.022 + 205.022i −0.329617 + 0.329617i
\(623\) −549.360 543.736i −0.881798 0.872771i
\(624\) 27.0035i 0.0432748i
\(625\) −416.845 + 465.688i −0.666952 + 0.745100i
\(626\) −170.822 + 295.872i −0.272878 + 0.472638i
\(627\) 2.04281 + 7.62387i 0.00325807 + 0.0121593i
\(628\) 55.8800 208.547i 0.0889809 0.332081i
\(629\) 58.5679i 0.0931128i
\(630\) −6.89986 + 148.332i −0.0109522 + 0.235448i
\(631\) 711.319 1.12729 0.563644 0.826017i \(-0.309399\pi\)
0.563644 + 0.826017i \(0.309399\pi\)
\(632\) 140.668 + 37.6919i 0.222576 + 0.0596392i
\(633\) −179.593 + 48.1217i −0.283717 + 0.0760216i
\(634\) 285.483 + 164.824i 0.450289 + 0.259974i
\(635\) 590.392 125.943i 0.929751 0.198336i
\(636\) −260.431 −0.409483
\(637\) 184.974 + 47.5291i 0.290384 + 0.0746140i
\(638\) −345.623 345.623i −0.541729 0.541729i
\(639\) −52.8357 + 30.5047i −0.0826851 + 0.0477382i
\(640\) 42.0109 37.8825i 0.0656420 0.0591914i
\(641\) −75.2839 + 130.395i −0.117448 + 0.203425i −0.918755 0.394827i \(-0.870805\pi\)
0.801308 + 0.598252i \(0.204138\pi\)
\(642\) −263.492 70.6024i −0.410423 0.109973i
\(643\) −569.798 569.798i −0.886155 0.886155i 0.107996 0.994151i \(-0.465557\pi\)
−0.994151 + 0.107996i \(0.965557\pi\)
\(644\) 171.450 + 97.8137i 0.266226 + 0.151885i
\(645\) −65.3760 128.076i −0.101358 0.198567i
\(646\) −5.60909 9.71523i −0.00868280 0.0150390i
\(647\) 99.5449 + 371.507i 0.153856 + 0.574199i 0.999201 + 0.0399772i \(0.0127285\pi\)
−0.845345 + 0.534222i \(0.820605\pi\)
\(648\) 24.5885 6.58846i 0.0379452 0.0101674i
\(649\) 451.762 260.825i 0.696089 0.401887i
\(650\) 80.8344 111.602i 0.124361 0.171696i
\(651\) −184.776 + 0.950728i −0.283834 + 0.00146041i
\(652\) 426.492 426.492i 0.654129 0.654129i
\(653\) 23.7561 88.6589i 0.0363799 0.135772i −0.945347 0.326065i \(-0.894277\pi\)
0.981727 + 0.190293i \(0.0609439\pi\)
\(654\) −161.405 93.1873i −0.246797 0.142488i
\(655\) 56.5455 1094.27i 0.0863290 1.67065i
\(656\) 58.1588 + 100.734i 0.0886567 + 0.153558i
\(657\) 124.273 124.273i 0.189152 0.189152i
\(658\) −212.707 + 810.490i −0.323262 + 1.23175i
\(659\) 478.694i 0.726395i 0.931712 + 0.363197i \(0.118315\pi\)
−0.931712 + 0.363197i \(0.881685\pi\)
\(660\) 241.287 51.4717i 0.365586 0.0779874i
\(661\) 28.9020 50.0598i 0.0437247 0.0757334i −0.843335 0.537389i \(-0.819411\pi\)
0.887060 + 0.461655i \(0.152744\pi\)
\(662\) −133.828 499.452i −0.202157 0.754460i
\(663\) 43.3240 161.687i 0.0653453 0.243872i
\(664\) 331.436i 0.499151i
\(665\) 2.39232 + 10.9385i 0.00359748 + 0.0164488i
\(666\) −10.0213 −0.0150470
\(667\) 330.450 + 88.5438i 0.495427 + 0.132749i
\(668\) 152.399 40.8352i 0.228142 0.0611305i
\(669\) −323.683 186.879i −0.483831 0.279340i
\(670\) 263.025 405.672i 0.392574 0.605481i
\(671\) 1544.66 2.30203
\(672\) −48.2473 + 48.7463i −0.0717965 + 0.0725392i
\(673\) 351.482 + 351.482i 0.522261 + 0.522261i 0.918254 0.395993i \(-0.129599\pi\)
−0.395993 + 0.918254i \(0.629599\pi\)
\(674\) 680.453 392.860i 1.00957 0.582878i
\(675\) −121.344 46.3758i −0.179768 0.0687049i
\(676\) 153.809 266.404i 0.227528 0.394089i
\(677\) 660.882 + 177.083i 0.976192 + 0.261570i 0.711440 0.702747i \(-0.248043\pi\)
0.264752 + 0.964317i \(0.414710\pi\)
\(678\) 187.598 + 187.598i 0.276694 + 0.276694i
\(679\) −587.220 335.015i −0.864831 0.493395i
\(680\) −312.325 + 159.425i −0.459301 + 0.234449i
\(681\) −279.236 483.651i −0.410038 0.710207i
\(682\) 79.4584 + 296.543i 0.116508 + 0.434814i
\(683\) −413.953 + 110.918i −0.606080 + 0.162399i −0.548792 0.835959i \(-0.684912\pi\)
−0.0572882 + 0.998358i \(0.518245\pi\)
\(684\) 1.66233 0.959746i 0.00243030 0.00140314i
\(685\) −318.659 + 983.178i −0.465195 + 1.43530i
\(686\) 248.993 + 416.294i 0.362963 + 0.606842i
\(687\) 113.612 113.612i 0.165374 0.165374i
\(688\) 17.1899 64.1536i 0.0249853 0.0932466i
\(689\) −253.765 146.511i −0.368310 0.212644i
\(690\) −128.241 + 115.639i −0.185857 + 0.167593i
\(691\) 118.514 + 205.272i 0.171510 + 0.297065i 0.938948 0.344059i \(-0.111802\pi\)
−0.767438 + 0.641124i \(0.778469\pi\)
\(692\) −296.430 + 296.430i −0.428367 + 0.428367i
\(693\) −288.532 + 78.9054i −0.416353 + 0.113861i
\(694\) 401.758i 0.578902i
\(695\) −591.796 + 912.747i −0.851505 + 1.31331i
\(696\) −59.4350 + 102.944i −0.0853951 + 0.147909i
\(697\) −186.618 696.469i −0.267745 0.999238i
\(698\) 126.393 471.703i 0.181078 0.675793i
\(699\) 658.240i 0.941688i
\(700\) 345.322 57.0355i 0.493316 0.0814793i
\(701\) 179.002 0.255352 0.127676 0.991816i \(-0.459248\pi\)
0.127676 + 0.991816i \(0.459248\pi\)
\(702\) 27.6656 + 7.41297i 0.0394096 + 0.0105598i
\(703\) −0.729905 + 0.195577i −0.00103827 + 0.000278204i
\(704\) 98.6863 + 56.9766i 0.140179 + 0.0809326i
\(705\) −615.073 398.793i −0.872443 0.565664i
\(706\) 835.724 1.18374
\(707\) −676.619 177.573i −0.957029 0.251165i
\(708\) −89.7053 89.7053i −0.126702 0.126702i
\(709\) −614.815 + 354.963i −0.867158 + 0.500654i −0.866403 0.499346i \(-0.833574\pi\)
−0.000754991 1.00000i \(0.500240\pi\)
\(710\) 96.2996 + 106.794i 0.135633 + 0.150414i
\(711\) 77.2322 133.770i 0.108625 0.188144i
\(712\) 301.675 + 80.8337i 0.423701 + 0.113530i
\(713\) −151.940 151.940i −0.213100 0.213100i
\(714\) 367.095 214.468i 0.514139 0.300376i
\(715\) 264.067 + 85.5871i 0.369325 + 0.119702i
\(716\) 150.138 + 260.047i 0.209690 + 0.363194i
\(717\) −87.9976 328.412i −0.122730 0.458036i
\(718\) −565.482 + 151.521i −0.787580 + 0.211031i
\(719\) −281.298 + 162.407i −0.391235 + 0.225880i −0.682695 0.730703i \(-0.739192\pi\)
0.291460 + 0.956583i \(0.405859\pi\)
\(720\) −27.2785 53.4404i −0.0378869 0.0742228i
\(721\) 783.907 4.03344i 1.08725 0.00559423i
\(722\) −360.898 + 360.898i −0.499858 + 0.499858i
\(723\) 168.717 629.660i 0.233357 0.870898i
\(724\) 254.896 + 147.164i 0.352067 + 0.203266i
\(725\) 553.800 247.540i 0.763863 0.341434i
\(726\) 100.301 + 173.727i 0.138156 + 0.239293i
\(727\) 32.6420 32.6420i 0.0448996 0.0448996i −0.684301 0.729200i \(-0.739892\pi\)
0.729200 + 0.684301i \(0.239892\pi\)
\(728\) −74.4356 + 20.3560i −0.102247 + 0.0279616i
\(729\) 27.0000i 0.0370370i
\(730\) −347.578 225.358i −0.476134 0.308710i
\(731\) −205.854 + 356.550i −0.281606 + 0.487757i
\(732\) −97.2263 362.853i −0.132823 0.495701i
\(733\) −70.6890 + 263.815i −0.0964379 + 0.359911i −0.997234 0.0743321i \(-0.976318\pi\)
0.900796 + 0.434243i \(0.142984\pi\)
\(734\) 602.691i 0.821105i
\(735\) −414.082 + 92.7975i −0.563376 + 0.126255i
\(736\) −79.7573 −0.108366
\(737\) 940.747 + 252.072i 1.27645 + 0.342025i
\(738\) 119.170 31.9314i 0.161476 0.0432675i
\(739\) 852.048 + 491.930i 1.15297 + 0.665670i 0.949610 0.313434i \(-0.101479\pi\)
0.203364 + 0.979103i \(0.434813\pi\)
\(740\) 4.92787 + 23.1007i 0.00665928 + 0.0312171i
\(741\) 2.15971 0.00291458
\(742\) −196.321 717.885i −0.264584 0.967499i
\(743\) 121.603 + 121.603i 0.163664 + 0.163664i 0.784188 0.620524i \(-0.213080\pi\)
−0.620524 + 0.784188i \(0.713080\pi\)
\(744\) 64.6590 37.3309i 0.0869072 0.0501759i
\(745\) −1169.10 60.4122i −1.56927 0.0810902i
\(746\) −114.052 + 197.543i −0.152884 + 0.264803i
\(747\) −339.563 90.9855i −0.454568 0.121801i
\(748\) −499.486 499.486i −0.667763 0.667763i
\(749\) −4.01098 779.542i −0.00535512 1.04078i
\(750\) −47.2340 + 302.521i −0.0629787 + 0.403361i
\(751\) 340.967 + 590.571i 0.454017 + 0.786380i 0.998631 0.0523066i \(-0.0166573\pi\)
−0.544614 + 0.838687i \(0.683324\pi\)
\(752\) −87.6303 327.041i −0.116530 0.434895i
\(753\) 323.017 86.5522i 0.428974 0.114943i
\(754\) −115.827 + 66.8730i −0.153617 + 0.0886909i
\(755\) 1012.37 516.763i 1.34089 0.684455i
\(756\) 36.6967 + 62.8120i 0.0485407 + 0.0830847i
\(757\) −734.889 + 734.889i −0.970792 + 0.970792i −0.999585 0.0287938i \(-0.990833\pi\)
0.0287938 + 0.999585i \(0.490833\pi\)
\(758\) −84.2852 + 314.557i −0.111194 + 0.414983i
\(759\) −301.247 173.925i −0.396900 0.229150i
\(760\) −3.02980 3.35998i −0.00398658 0.00442103i
\(761\) −62.7638 108.710i −0.0824755 0.142852i 0.821837 0.569722i \(-0.192949\pi\)
−0.904313 + 0.426871i \(0.859616\pi\)
\(762\) 209.119 209.119i 0.274435 0.274435i
\(763\) 135.201 515.164i 0.177196 0.675182i
\(764\) 448.506i 0.587049i
\(765\) 77.5952 + 363.748i 0.101432 + 0.475487i
\(766\) 102.749 177.967i 0.134138 0.232333i
\(767\) −36.9435 137.875i −0.0481662 0.179759i
\(768\) 7.17260 26.7685i 0.00933933 0.0348548i
\(769\) 1052.67i 1.36888i −0.729067 0.684442i \(-0.760046\pi\)
0.729067 0.684442i \(-0.239954\pi\)
\(770\) 323.772 + 626.311i 0.420483 + 0.813391i
\(771\) −373.871 −0.484917
\(772\) 31.5934 + 8.46543i 0.0409241 + 0.0109656i
\(773\) 610.760 163.653i 0.790116 0.211711i 0.158876 0.987299i \(-0.449213\pi\)
0.631240 + 0.775588i \(0.282546\pi\)
\(774\) −61.0077 35.2228i −0.0788213 0.0455075i
\(775\) −378.977 39.2714i −0.489003 0.0506727i
\(776\) 273.171 0.352025
\(777\) −7.55435 27.6239i −0.00972246 0.0355520i
\(778\) −479.067 479.067i −0.615767 0.615767i
\(779\) 8.05659 4.65147i 0.0103422 0.00597108i
\(780\) 3.48379 67.4187i 0.00446640 0.0864343i
\(781\) −144.838 + 250.867i −0.185452 + 0.321212i
\(782\) 477.558 + 127.961i 0.610688 + 0.163633i
\(783\) 89.1525 + 89.1525i 0.113860 + 0.113860i
\(784\) −170.740 96.2481i −0.217781 0.122765i
\(785\) −166.419 + 513.464i −0.211999 + 0.654094i
\(786\) −268.399 464.881i −0.341475 0.591451i
\(787\) 297.140 + 1108.94i 0.377561 + 1.40908i 0.849567 + 0.527480i \(0.176863\pi\)
−0.472007 + 0.881595i \(0.656470\pi\)
\(788\) −545.103 + 146.060i −0.691755 + 0.185355i
\(789\) 672.412 388.217i 0.852233 0.492037i
\(790\) −346.339 112.252i −0.438404 0.142092i
\(791\) −375.702 + 658.536i −0.474970 + 0.832536i
\(792\) 85.4649 85.4649i 0.107910 0.107910i
\(793\) 109.394 408.262i 0.137949 0.514833i
\(794\) 10.8098 + 6.24106i 0.0136144 + 0.00786028i
\(795\) 650.211 + 33.5990i 0.817875 + 0.0422629i
\(796\) 42.8941 + 74.2948i 0.0538871 + 0.0933352i
\(797\) −862.362 + 862.362i −1.08201 + 1.08201i −0.0856885 + 0.996322i \(0.527309\pi\)
−0.996322 + 0.0856885i \(0.972691\pi\)
\(798\) 3.89867 + 3.85876i 0.00488555 + 0.00483554i
\(799\) 2098.80i 2.62678i
\(800\) −109.775 + 89.1601i −0.137218 + 0.111450i
\(801\) 165.631 286.882i 0.206781 0.358155i
\(802\) −290.618 1084.60i −0.362366 1.35237i
\(803\) 215.974 806.028i 0.268960 1.00377i
\(804\) 236.855i 0.294596i
\(805\) −415.434 266.328i −0.516067 0.330842i
\(806\) 84.0052 0.104225
\(807\) −179.770 48.1692i −0.222763 0.0596892i
\(808\) 273.023 73.1562i 0.337899 0.0905398i
\(809\) −16.9629 9.79354i −0.0209677 0.0121057i 0.489479 0.872015i \(-0.337187\pi\)
−0.510447 + 0.859909i \(0.670520\pi\)
\(810\) −62.2392 + 13.2770i −0.0768386 + 0.0163913i
\(811\) 785.632 0.968721 0.484360 0.874869i \(-0.339052\pi\)
0.484360 + 0.874869i \(0.339052\pi\)
\(812\) −328.572 86.2312i −0.404646 0.106196i
\(813\) 240.147 + 240.147i 0.295383 + 0.295383i
\(814\) −41.2069 + 23.7908i −0.0506227 + 0.0292270i
\(815\) −1119.83 + 1009.79i −1.37403 + 1.23900i
\(816\) −85.8940 + 148.773i −0.105262 + 0.182320i
\(817\) −5.13093 1.37483i −0.00628021 0.00168278i
\(818\) −602.576 602.576i −0.736645 0.736645i
\(819\) 0.421137 + 81.8488i 0.000514209 + 0.0999375i
\(820\) −132.207 259.003i −0.161228 0.315857i
\(821\) −689.847 1194.85i −0.840252 1.45536i −0.889681 0.456582i \(-0.849073\pi\)
0.0494290 0.998778i \(-0.484260\pi\)
\(822\) 131.046 + 489.071i 0.159424 + 0.594977i
\(823\) 583.631 156.383i 0.709151 0.190016i 0.113825 0.993501i \(-0.463690\pi\)
0.595326 + 0.803484i \(0.297023\pi\)
\(824\) −274.314 + 158.375i −0.332905 + 0.192203i
\(825\) −609.054 + 97.3787i −0.738247 + 0.118035i
\(826\) 179.652 314.897i 0.217496 0.381231i
\(827\) 337.261 337.261i 0.407812 0.407812i −0.473163 0.880975i \(-0.656888\pi\)
0.880975 + 0.473163i \(0.156888\pi\)
\(828\) −21.8949 + 81.7128i −0.0264431 + 0.0986870i
\(829\) 594.040 + 342.969i 0.716574 + 0.413714i 0.813490 0.581578i \(-0.197565\pi\)
−0.0969163 + 0.995293i \(0.530898\pi\)
\(830\) −42.7595 + 827.486i −0.0515175 + 0.996971i
\(831\) 322.656 + 558.857i 0.388275 + 0.672511i
\(832\) 22.0482 22.0482i 0.0265003 0.0265003i
\(833\) 867.914 + 850.233i 1.04191 + 1.02069i
\(834\) 532.916i 0.638988i
\(835\) −385.758 + 82.2905i −0.461986 + 0.0985515i
\(836\) 4.55692 7.89282i 0.00545086 0.00944117i
\(837\) −20.4961 76.4924i −0.0244875 0.0913887i
\(838\) −124.966 + 466.380i −0.149124 + 0.556540i
\(839\) 1160.13i 1.38275i −0.722494 0.691377i \(-0.757004\pi\)
0.722494 0.691377i \(-0.242996\pi\)
\(840\) 126.746 115.479i 0.150888 0.137475i
\(841\) 252.247 0.299937
\(842\) 128.870 + 34.5306i 0.153052 + 0.0410102i
\(843\) 429.348 115.043i 0.509309 0.136469i
\(844\) 185.928 + 107.346i 0.220294 + 0.127187i
\(845\) −418.379 + 645.280i −0.495123 + 0.763645i
\(846\) −359.116 −0.424487
\(847\) −403.272 + 407.443i −0.476118 + 0.481043i
\(848\) 212.641 + 212.641i 0.250756 + 0.250756i
\(849\) −623.379 + 359.908i −0.734251 + 0.423920i
\(850\) 800.339 357.738i 0.941575 0.420869i
\(851\) 16.6515 28.8412i 0.0195670 0.0338910i
\(852\) 68.0472 + 18.2332i 0.0798676 + 0.0214005i
\(853\) −62.9769 62.9769i −0.0738299 0.0738299i 0.669228 0.743057i \(-0.266625\pi\)
−0.743057 + 0.669228i \(0.766625\pi\)
\(854\) 926.921 541.536i 1.08539 0.634117i
\(855\) −4.27410 + 2.18171i −0.00499895 + 0.00255170i
\(856\) 157.493 + 272.787i 0.183988 + 0.318676i
\(857\) 26.3303 + 98.2660i 0.0307238 + 0.114663i 0.979585 0.201031i \(-0.0644293\pi\)
−0.948861 + 0.315694i \(0.897763\pi\)
\(858\) 131.357 35.1971i 0.153097 0.0410223i
\(859\) −611.105 + 352.822i −0.711415 + 0.410735i −0.811585 0.584235i \(-0.801395\pi\)
0.100170 + 0.994970i \(0.468061\pi\)
\(860\) −51.1942 + 157.953i −0.0595281 + 0.183666i
\(861\) 177.853 + 304.423i 0.206566 + 0.353569i
\(862\) 298.198 298.198i 0.345937 0.345937i
\(863\) −184.835 + 689.815i −0.214178 + 0.799322i 0.772277 + 0.635286i \(0.219118\pi\)
−0.986454 + 0.164036i \(0.947549\pi\)
\(864\) −25.4558 14.6969i −0.0294628 0.0170103i
\(865\) 778.331 701.844i 0.899805 0.811381i
\(866\) 466.639 + 808.243i 0.538844 + 0.933306i
\(867\) 399.041 399.041i 0.460254 0.460254i
\(868\) 151.645 + 150.093i 0.174706 + 0.172918i
\(869\) 733.405i 0.843964i
\(870\) 161.671 249.350i 0.185828 0.286610i
\(871\) 133.248 230.793i 0.152983 0.264975i
\(872\) 55.6996 + 207.874i 0.0638757 + 0.238387i
\(873\) 74.9907 279.869i 0.0859000 0.320583i
\(874\) 6.37889i 0.00729850i
\(875\) −869.512 + 97.8479i −0.993728 + 0.111826i
\(876\) −202.937 −0.231663
\(877\) 949.597 + 254.444i 1.08278 + 0.290130i 0.755733 0.654879i \(-0.227281\pi\)
0.327045 + 0.945009i \(0.393947\pi\)
\(878\) 104.489 27.9978i 0.119008 0.0318882i
\(879\) −501.107 289.315i −0.570088 0.329141i
\(880\) −239.036 154.983i −0.271632 0.176118i
\(881\) −453.529 −0.514789 −0.257395 0.966306i \(-0.582864\pi\)
−0.257395 + 0.966306i \(0.582864\pi\)
\(882\) −145.480 + 148.505i −0.164943 + 0.168373i
\(883\) 53.9427 + 53.9427i 0.0610903 + 0.0610903i 0.736992 0.675902i \(-0.236246\pi\)
−0.675902 + 0.736992i \(0.736246\pi\)
\(884\) −167.391 + 96.6432i −0.189356 + 0.109325i
\(885\) 212.391 + 235.538i 0.239990 + 0.266144i
\(886\) 149.352 258.685i 0.168569 0.291970i
\(887\) −1490.91 399.489i −1.68085 0.450382i −0.712846 0.701321i \(-0.752594\pi\)
−0.968003 + 0.250939i \(0.919261\pi\)
\(888\) 8.18235 + 8.18235i 0.00921436 + 0.00921436i
\(889\) 734.083 + 418.802i 0.825740 + 0.471093i
\(890\) −742.755 240.735i −0.834556 0.270489i
\(891\) −64.0987 111.022i −0.0719401 0.124604i
\(892\) 111.700 + 416.872i 0.125225 + 0.467345i
\(893\) −26.1563 + 7.00857i −0.0292904 + 0.00784834i
\(894\) −496.670 + 286.753i −0.555559 + 0.320752i
\(895\) −341.296 668.621i −0.381336 0.747063i
\(896\) 79.1949 0.407482i 0.0883872 0.000454779i
\(897\) −67.3038 + 67.3038i −0.0750321 + 0.0750321i
\(898\) 146.751 547.681i 0.163419 0.609889i
\(899\) 320.250 + 184.897i 0.356230 + 0.205669i
\(900\) 61.2110 + 136.942i 0.0680122 + 0.152158i
\(901\) −932.063 1614.38i −1.03448 1.79176i
\(902\) 414.211 414.211i 0.459214 0.459214i
\(903\) 51.1030 194.721i 0.0565924 0.215638i
\(904\) 306.347i 0.338879i
\(905\) −617.406 400.306i −0.682216 0.442327i
\(906\) 278.418 482.234i 0.307305 0.532267i
\(907\) 294.855 + 1100.41i 0.325088 + 1.21324i 0.914223 + 0.405210i \(0.132802\pi\)
−0.589136 + 0.808034i \(0.700532\pi\)
\(908\) −166.904 + 622.894i −0.183815 + 0.686007i
\(909\) 299.800i 0.329813i
\(910\) 188.467 41.2191i 0.207107 0.0452957i
\(911\) −848.410 −0.931296 −0.465648 0.884970i \(-0.654179\pi\)
−0.465648 + 0.884970i \(0.654179\pi\)
\(912\) −2.14091 0.573656i −0.00234749 0.000629009i
\(913\) −1612.26 + 432.004i −1.76589 + 0.473169i
\(914\) 896.610 + 517.658i 0.980974 + 0.566366i
\(915\) 195.929 + 918.468i 0.214130 + 1.00379i
\(916\) −185.527 −0.202541
\(917\) 1079.13 1090.29i 1.17680 1.18897i
\(918\) 128.841 + 128.841i 0.140350 + 0.140350i
\(919\) 73.9472 42.6934i 0.0804649 0.0464564i −0.459228 0.888319i \(-0.651874\pi\)
0.539693 + 0.841862i \(0.318540\pi\)
\(920\) 199.127 + 10.2897i 0.216443 + 0.0111845i
\(921\) 130.469 225.979i 0.141660 0.245362i
\(922\) −624.441 167.318i −0.677268 0.181473i
\(923\) 56.0480 + 56.0480i 0.0607237 + 0.0607237i
\(924\) 300.012 + 171.160i 0.324688 + 0.185238i
\(925\) −9.32297 58.3104i −0.0100789 0.0630383i
\(926\) −409.466 709.216i −0.442188 0.765892i
\(927\) 86.9541 + 324.517i 0.0938016 + 0.350072i
\(928\) 132.582 35.5253i 0.142869 0.0382816i
\(929\) 546.812 315.702i 0.588603 0.339830i −0.175942 0.984401i \(-0.556297\pi\)
0.764545 + 0.644571i \(0.222964\pi\)
\(930\) −166.248 + 84.8610i −0.178761 + 0.0912484i
\(931\) −7.69781 + 13.6556i −0.00826833 + 0.0146677i
\(932\) −537.451 + 537.451i −0.576664 + 0.576664i
\(933\) 91.9088 343.008i 0.0985089 0.367640i
\(934\) 177.734 + 102.615i 0.190293 + 0.109866i
\(935\) 1182.61 + 1311.49i 1.26483 + 1.40267i
\(936\) −16.5362 28.6415i −0.0176669 0.0305999i
\(937\) −481.721 + 481.721i −0.514110 + 0.514110i −0.915783 0.401673i \(-0.868429\pi\)
0.401673 + 0.915783i \(0.368429\pi\)
\(938\) 652.897 178.549i 0.696052 0.190350i
\(939\) 418.426i 0.445608i
\(940\) 176.591 + 827.818i 0.187863 + 0.880657i
\(941\) 458.205 793.634i 0.486934 0.843395i −0.512953 0.858417i \(-0.671449\pi\)
0.999887 + 0.0150221i \(0.00478185\pi\)
\(942\) 68.4387 + 255.417i 0.0726526 + 0.271143i
\(943\) −106.115 + 396.027i −0.112529 + 0.419965i
\(944\) 146.488i 0.155178i
\(945\) −83.5160 161.555i −0.0883768 0.170958i
\(946\) −334.479 −0.353572
\(947\) 940.527 + 252.013i 0.993164 + 0.266118i 0.718579 0.695445i \(-0.244793\pi\)
0.274585 + 0.961563i \(0.411459\pi\)
\(948\) −172.283 + 46.1630i −0.181733 + 0.0486952i
\(949\) −197.742 114.167i −0.208369 0.120302i
\(950\) 7.13092 + 8.77965i 0.00750623 + 0.00924173i
\(951\) −403.734 −0.424536
\(952\) −474.845 124.619i −0.498787 0.130903i
\(953\) 451.156 + 451.156i 0.473407 + 0.473407i 0.903015 0.429609i \(-0.141348\pi\)
−0.429609 + 0.903015i \(0.641348\pi\)
\(954\) 276.229 159.481i 0.289548 0.167171i
\(955\) −57.8630 + 1119.77i −0.0605895 + 1.17253i
\(956\) −196.297 + 339.997i −0.205332 + 0.355645i
\(957\) 578.239 + 154.939i 0.604221 + 0.161900i
\(958\) 148.290 + 148.290i 0.154791 + 0.154791i
\(959\) −1249.35 + 729.908i −1.30276 + 0.761114i
\(960\) −21.3611 + 65.9068i −0.0222511 + 0.0686529i
\(961\) 364.367 + 631.103i 0.379154 + 0.656714i
\(962\) 3.36975 + 12.5761i 0.00350286 + 0.0130728i
\(963\) 322.710 86.4699i 0.335109 0.0897922i
\(964\) −651.872 + 376.358i −0.676215 + 0.390413i
\(965\) −77.7862 25.2113i −0.0806074 0.0261257i
\(966\) −241.748 + 1.24387i −0.250257 + 0.00128765i
\(967\) −1040.28 + 1040.28i −1.07578 + 1.07578i −0.0788960 + 0.996883i \(0.525139\pi\)
−0.996883 + 0.0788960i \(0.974861\pi\)
\(968\) 59.9518 223.743i 0.0619337 0.231140i
\(969\) 11.8987 + 6.86970i 0.0122793 + 0.00708948i
\(970\) −682.018 35.2426i −0.703111 0.0363326i
\(971\) −295.722 512.205i −0.304554 0.527503i 0.672608 0.739999i \(-0.265174\pi\)
−0.977162 + 0.212496i \(0.931841\pi\)
\(972\) −22.0454 + 22.0454i −0.0226805 + 0.0226805i
\(973\) −1468.99 + 401.728i −1.50976 + 0.412875i
\(974\) 472.639i 0.485256i
\(975\) −17.3958 + 167.873i −0.0178418 + 0.172177i
\(976\) −216.884 + 375.653i −0.222217 + 0.384891i
\(977\) 14.4319 + 53.8605i 0.0147716 + 0.0551284i 0.972918 0.231149i \(-0.0742486\pi\)
−0.958147 + 0.286278i \(0.907582\pi\)
\(978\) −191.191 + 713.536i −0.195492 + 0.729586i
\(979\) 1572.85i 1.60659i
\(980\) 413.865 + 262.327i 0.422311 + 0.267681i
\(981\) 228.261 0.232682
\(982\) 330.531 + 88.5655i 0.336590 + 0.0901889i
\(983\) 1031.17 276.301i 1.04900 0.281079i 0.307162 0.951657i \(-0.400621\pi\)
0.741839 + 0.670578i \(0.233954\pi\)
\(984\) −123.373 71.2297i −0.125380 0.0723879i
\(985\) 1379.79 294.338i 1.40080 0.298820i
\(986\) −850.852 −0.862933
\(987\) −270.712 989.910i −0.274278 1.00295i
\(988\) −1.76339 1.76339i −0.00178481 0.00178481i
\(989\) 202.742 117.053i 0.204997 0.118355i
\(990\) −224.404 + 202.351i −0.226670 + 0.204395i
\(991\) −924.731 + 1601.68i −0.933130 + 1.61623i −0.155194 + 0.987884i \(0.549600\pi\)
−0.777936 + 0.628344i \(0.783733\pi\)
\(992\) −83.2743 22.3133i −0.0839459 0.0224932i
\(993\) 447.797 + 447.797i 0.450953 + 0.450953i
\(994\) 1.03584 + 201.318i 0.00104210 + 0.202534i
\(995\) −97.5075 191.023i −0.0979974 0.191983i
\(996\) 202.962 + 351.541i 0.203777 + 0.352953i
\(997\) 119.126 + 444.584i 0.119484 + 0.445922i 0.999583 0.0288686i \(-0.00919045\pi\)
−0.880099 + 0.474791i \(0.842524\pi\)
\(998\) 912.515 244.508i 0.914344 0.244998i
\(999\) 10.6292 6.13676i 0.0106398 0.00614291i
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 210.3.v.b.193.2 yes 32
5.2 odd 4 inner 210.3.v.b.67.6 yes 32
7.2 even 3 inner 210.3.v.b.163.6 yes 32
35.2 odd 12 inner 210.3.v.b.37.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.v.b.37.2 32 35.2 odd 12 inner
210.3.v.b.67.6 yes 32 5.2 odd 4 inner
210.3.v.b.163.6 yes 32 7.2 even 3 inner
210.3.v.b.193.2 yes 32 1.1 even 1 trivial