Properties

Label 770.2.m.e.43.1
Level $770$
Weight $2$
Character 770.43
Analytic conductor $6.148$
Analytic rank $0$
Dimension $16$
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] = [770,2,Mod(43,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.m (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: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 32x^{14} + 404x^{12} + 2600x^{10} + 9170x^{8} + 17648x^{6} + 17180x^{4} + 6904x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(0.914718i\) of defining polynomial
Character \(\chi\) \(=\) 770.43
Dual form 770.2.m.e.197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-2.14984 - 2.14984i) q^{3} +1.00000i q^{4} +(-1.71500 - 1.43484i) q^{5} +3.04034i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +6.24365i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-2.14984 - 2.14984i) q^{3} +1.00000i q^{4} +(-1.71500 - 1.43484i) q^{5} +3.04034i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +6.24365i q^{9} +(0.198102 + 2.22728i) q^{10} +(0.280159 + 3.30477i) q^{11} +(2.14984 - 2.14984i) q^{12} +(3.30477 - 3.30477i) q^{13} -1.00000i q^{14} +(0.602298 + 6.77167i) q^{15} -1.00000 q^{16} +(2.29361 + 2.29361i) q^{17} +(4.41493 - 4.41493i) q^{18} -0.396205 q^{19} +(1.43484 - 1.71500i) q^{20} -3.04034i q^{21} +(2.13872 - 2.53493i) q^{22} +(5.93428 + 5.93428i) q^{23} -3.04034 q^{24} +(0.882457 + 4.92151i) q^{25} -4.67365 q^{26} +(6.97334 - 6.97334i) q^{27} +(-0.707107 + 0.707107i) q^{28} -4.95580 q^{29} +(4.36240 - 5.21418i) q^{30} +3.24365 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.50244 - 7.70704i) q^{33} -3.24365i q^{34} +(-0.198102 - 2.22728i) q^{35} -6.24365 q^{36} +(-5.43000 + 5.43000i) q^{37} +(0.280159 + 0.280159i) q^{38} -14.2095 q^{39} +(-2.22728 + 0.198102i) q^{40} -6.00143i q^{41} +(-2.14984 + 2.14984i) q^{42} +(7.83946 - 7.83946i) q^{43} +(-3.30477 + 0.280159i) q^{44} +(8.95865 - 10.7079i) q^{45} -8.39234i q^{46} +(-3.29969 + 3.29969i) q^{47} +(2.14984 + 2.14984i) q^{48} +1.00000i q^{49} +(2.85604 - 4.10403i) q^{50} -9.86179i q^{51} +(3.30477 + 3.30477i) q^{52} +(-9.91730 - 9.91730i) q^{53} -9.86179 q^{54} +(4.26135 - 6.06967i) q^{55} +1.00000 q^{56} +(0.851778 + 0.851778i) q^{57} +(3.50428 + 3.50428i) q^{58} +12.4521i q^{59} +(-6.77167 + 0.602298i) q^{60} +7.90478i q^{61} +(-2.29361 - 2.29361i) q^{62} +(-4.41493 + 4.41493i) q^{63} -1.00000i q^{64} +(-10.4095 + 0.925861i) q^{65} +(-10.0476 + 0.851778i) q^{66} +(8.03905 - 8.03905i) q^{67} +(-2.29361 + 2.29361i) q^{68} -25.5156i q^{69} +(-1.43484 + 1.71500i) q^{70} +6.66397 q^{71} +(4.41493 + 4.41493i) q^{72} +(3.89212 - 3.89212i) q^{73} +7.67918 q^{74} +(8.68333 - 12.4776i) q^{75} -0.396205i q^{76} +(-2.13872 + 2.53493i) q^{77} +(10.0476 + 10.0476i) q^{78} +14.1181 q^{79} +(1.71500 + 1.43484i) q^{80} -11.2522 q^{81} +(-4.24365 + 4.24365i) q^{82} +(-1.89651 + 1.89651i) q^{83} +3.04034 q^{84} +(-0.642575 - 7.22450i) q^{85} -11.0867 q^{86} +(10.6542 + 10.6542i) q^{87} +(2.53493 + 2.13872i) q^{88} +5.86857i q^{89} +(-13.9063 + 1.23688i) q^{90} +4.67365 q^{91} +(-5.93428 + 5.93428i) q^{92} +(-6.97334 - 6.97334i) q^{93} +4.66646 q^{94} +(0.679492 + 0.568491i) q^{95} -3.04034i q^{96} +(3.24365 - 3.24365i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-20.6338 + 1.74921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{3} - 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{3} - 8 q^{5} - 8 q^{11} + 8 q^{12} + 24 q^{15} - 16 q^{16} + 16 q^{20} - 8 q^{22} + 32 q^{23} + 16 q^{25} + 16 q^{26} - 32 q^{27} - 24 q^{33} - 48 q^{36} - 48 q^{37} - 8 q^{38} - 8 q^{42} + 72 q^{45} + 8 q^{48} - 16 q^{53} - 48 q^{55} + 16 q^{56} + 32 q^{58} - 56 q^{60} - 32 q^{66} + 48 q^{67} - 16 q^{70} - 48 q^{71} + 112 q^{75} + 8 q^{77} + 32 q^{78} + 8 q^{80} - 80 q^{81} - 16 q^{82} + 32 q^{86} - 8 q^{88} - 16 q^{91} - 32 q^{92} + 32 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −2.14984 2.14984i −1.24121 1.24121i −0.959498 0.281714i \(-0.909097\pi\)
−0.281714 0.959498i \(-0.590903\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −1.71500 1.43484i −0.766972 0.641681i
\(6\) 3.04034i 1.24121i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 6.24365i 2.08122i
\(10\) 0.198102 + 2.22728i 0.0626455 + 0.704326i
\(11\) 0.280159 + 3.30477i 0.0844711 + 0.996426i
\(12\) 2.14984 2.14984i 0.620606 0.620606i
\(13\) 3.30477 3.30477i 0.916579 0.916579i −0.0802002 0.996779i \(-0.525556\pi\)
0.996779 + 0.0802002i \(0.0255560\pi\)
\(14\) 1.00000i 0.267261i
\(15\) 0.602298 + 6.77167i 0.155513 + 1.74844i
\(16\) −1.00000 −0.250000
\(17\) 2.29361 + 2.29361i 0.556281 + 0.556281i 0.928247 0.371965i \(-0.121316\pi\)
−0.371965 + 0.928247i \(0.621316\pi\)
\(18\) 4.41493 4.41493i 1.04061 1.04061i
\(19\) −0.396205 −0.0908956 −0.0454478 0.998967i \(-0.514471\pi\)
−0.0454478 + 0.998967i \(0.514471\pi\)
\(20\) 1.43484 1.71500i 0.320840 0.383486i
\(21\) 3.04034i 0.663456i
\(22\) 2.13872 2.53493i 0.455977 0.540449i
\(23\) 5.93428 + 5.93428i 1.23738 + 1.23738i 0.961066 + 0.276317i \(0.0891141\pi\)
0.276317 + 0.961066i \(0.410886\pi\)
\(24\) −3.04034 −0.620606
\(25\) 0.882457 + 4.92151i 0.176491 + 0.984302i
\(26\) −4.67365 −0.916579
\(27\) 6.97334 6.97334i 1.34202 1.34202i
\(28\) −0.707107 + 0.707107i −0.133631 + 0.133631i
\(29\) −4.95580 −0.920270 −0.460135 0.887849i \(-0.652199\pi\)
−0.460135 + 0.887849i \(0.652199\pi\)
\(30\) 4.36240 5.21418i 0.796462 0.951975i
\(31\) 3.24365 0.582577 0.291288 0.956635i \(-0.405916\pi\)
0.291288 + 0.956635i \(0.405916\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 6.50244 7.70704i 1.13193 1.34162i
\(34\) 3.24365i 0.556281i
\(35\) −0.198102 2.22728i −0.0334854 0.376478i
\(36\) −6.24365 −1.04061
\(37\) −5.43000 + 5.43000i −0.892687 + 0.892687i −0.994775 0.102088i \(-0.967448\pi\)
0.102088 + 0.994775i \(0.467448\pi\)
\(38\) 0.280159 + 0.280159i 0.0454478 + 0.0454478i
\(39\) −14.2095 −2.27534
\(40\) −2.22728 + 0.198102i −0.352163 + 0.0313227i
\(41\) 6.00143i 0.937265i −0.883393 0.468633i \(-0.844747\pi\)
0.883393 0.468633i \(-0.155253\pi\)
\(42\) −2.14984 + 2.14984i −0.331728 + 0.331728i
\(43\) 7.83946 7.83946i 1.19551 1.19551i 0.220009 0.975498i \(-0.429391\pi\)
0.975498 0.220009i \(-0.0706086\pi\)
\(44\) −3.30477 + 0.280159i −0.498213 + 0.0422356i
\(45\) 8.95865 10.7079i 1.33548 1.59623i
\(46\) 8.39234i 1.23738i
\(47\) −3.29969 + 3.29969i −0.481309 + 0.481309i −0.905549 0.424241i \(-0.860541\pi\)
0.424241 + 0.905549i \(0.360541\pi\)
\(48\) 2.14984 + 2.14984i 0.310303 + 0.310303i
\(49\) 1.00000i 0.142857i
\(50\) 2.85604 4.10403i 0.403905 0.580397i
\(51\) 9.86179i 1.38093i
\(52\) 3.30477 + 3.30477i 0.458289 + 0.458289i
\(53\) −9.91730 9.91730i −1.36225 1.36225i −0.871048 0.491198i \(-0.836559\pi\)
−0.491198 0.871048i \(-0.663441\pi\)
\(54\) −9.86179 −1.34202
\(55\) 4.26135 6.06967i 0.574600 0.818434i
\(56\) 1.00000 0.133631
\(57\) 0.851778 + 0.851778i 0.112821 + 0.112821i
\(58\) 3.50428 + 3.50428i 0.460135 + 0.460135i
\(59\) 12.4521i 1.62112i 0.585654 + 0.810561i \(0.300838\pi\)
−0.585654 + 0.810561i \(0.699162\pi\)
\(60\) −6.77167 + 0.602298i −0.874219 + 0.0777563i
\(61\) 7.90478i 1.01210i 0.862503 + 0.506052i \(0.168896\pi\)
−0.862503 + 0.506052i \(0.831104\pi\)
\(62\) −2.29361 2.29361i −0.291288 0.291288i
\(63\) −4.41493 + 4.41493i −0.556229 + 0.556229i
\(64\) 1.00000i 0.125000i
\(65\) −10.4095 + 0.925861i −1.29114 + 0.114839i
\(66\) −10.0476 + 0.851778i −1.23678 + 0.104847i
\(67\) 8.03905 8.03905i 0.982127 0.982127i −0.0177163 0.999843i \(-0.505640\pi\)
0.999843 + 0.0177163i \(0.00563957\pi\)
\(68\) −2.29361 + 2.29361i −0.278141 + 0.278141i
\(69\) 25.5156i 3.07171i
\(70\) −1.43484 + 1.71500i −0.171496 + 0.204982i
\(71\) 6.66397 0.790868 0.395434 0.918494i \(-0.370594\pi\)
0.395434 + 0.918494i \(0.370594\pi\)
\(72\) 4.41493 + 4.41493i 0.520304 + 0.520304i
\(73\) 3.89212 3.89212i 0.455538 0.455538i −0.441650 0.897187i \(-0.645607\pi\)
0.897187 + 0.441650i \(0.145607\pi\)
\(74\) 7.67918 0.892687
\(75\) 8.68333 12.4776i 1.00266 1.44079i
\(76\) 0.396205i 0.0454478i
\(77\) −2.13872 + 2.53493i −0.243730 + 0.288882i
\(78\) 10.0476 + 10.0476i 1.13767 + 1.13767i
\(79\) 14.1181 1.58841 0.794206 0.607648i \(-0.207887\pi\)
0.794206 + 0.607648i \(0.207887\pi\)
\(80\) 1.71500 + 1.43484i 0.191743 + 0.160420i
\(81\) −11.2522 −1.25025
\(82\) −4.24365 + 4.24365i −0.468633 + 0.468633i
\(83\) −1.89651 + 1.89651i −0.208169 + 0.208169i −0.803489 0.595320i \(-0.797025\pi\)
0.595320 + 0.803489i \(0.297025\pi\)
\(84\) 3.04034 0.331728
\(85\) −0.642575 7.22450i −0.0696970 0.783607i
\(86\) −11.0867 −1.19551
\(87\) 10.6542 + 10.6542i 1.14225 + 1.14225i
\(88\) 2.53493 + 2.13872i 0.270224 + 0.227989i
\(89\) 5.86857i 0.622067i 0.950399 + 0.311033i \(0.100675\pi\)
−0.950399 + 0.311033i \(0.899325\pi\)
\(90\) −13.9063 + 1.23688i −1.46586 + 0.130379i
\(91\) 4.67365 0.489932
\(92\) −5.93428 + 5.93428i −0.618692 + 0.618692i
\(93\) −6.97334 6.97334i −0.723101 0.723101i
\(94\) 4.66646 0.481309
\(95\) 0.679492 + 0.568491i 0.0697144 + 0.0583260i
\(96\) 3.04034i 0.310303i
\(97\) 3.24365 3.24365i 0.329343 0.329343i −0.522994 0.852337i \(-0.675185\pi\)
0.852337 + 0.522994i \(0.175185\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) −20.6338 + 1.74921i −2.07378 + 0.175803i
\(100\) −4.92151 + 0.882457i −0.492151 + 0.0882457i
\(101\) 2.98511i 0.297029i 0.988910 + 0.148515i \(0.0474492\pi\)
−0.988910 + 0.148515i \(0.952551\pi\)
\(102\) −6.97334 + 6.97334i −0.690463 + 0.690463i
\(103\) −2.43968 2.43968i −0.240389 0.240389i 0.576622 0.817011i \(-0.304371\pi\)
−0.817011 + 0.576622i \(0.804371\pi\)
\(104\) 4.67365i 0.458289i
\(105\) −4.36240 + 5.21418i −0.425727 + 0.508852i
\(106\) 14.0252i 1.36225i
\(107\) 2.33929 + 2.33929i 0.226147 + 0.226147i 0.811081 0.584934i \(-0.198880\pi\)
−0.584934 + 0.811081i \(0.698880\pi\)
\(108\) 6.97334 + 6.97334i 0.671010 + 0.671010i
\(109\) 9.86179 0.944588 0.472294 0.881441i \(-0.343426\pi\)
0.472294 + 0.881441i \(0.343426\pi\)
\(110\) −7.30513 + 1.27867i −0.696517 + 0.121917i
\(111\) 23.3473 2.21603
\(112\) −0.707107 0.707107i −0.0668153 0.0668153i
\(113\) 2.68333 + 2.68333i 0.252427 + 0.252427i 0.821965 0.569538i \(-0.192878\pi\)
−0.569538 + 0.821965i \(0.692878\pi\)
\(114\) 1.20460i 0.112821i
\(115\) −1.66254 18.6921i −0.155033 1.74304i
\(116\) 4.95580i 0.460135i
\(117\) 20.6338 + 20.6338i 1.90760 + 1.90760i
\(118\) 8.80495 8.80495i 0.810561 0.810561i
\(119\) 3.24365i 0.297345i
\(120\) 5.21418 + 4.36240i 0.475987 + 0.398231i
\(121\) −10.8430 + 1.85172i −0.985729 + 0.168338i
\(122\) 5.58952 5.58952i 0.506052 0.506052i
\(123\) −12.9021 + 12.9021i −1.16335 + 1.16335i
\(124\) 3.24365i 0.291288i
\(125\) 5.54818 9.70658i 0.496244 0.868183i
\(126\) 6.24365 0.556229
\(127\) −1.52521 1.52521i −0.135341 0.135341i 0.636191 0.771532i \(-0.280509\pi\)
−0.771532 + 0.636191i \(0.780509\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −33.7072 −2.96776
\(130\) 8.01532 + 6.70595i 0.702990 + 0.588151i
\(131\) 11.7099i 1.02310i −0.859254 0.511550i \(-0.829072\pi\)
0.859254 0.511550i \(-0.170928\pi\)
\(132\) 7.70704 + 6.50244i 0.670811 + 0.565965i
\(133\) −0.280159 0.280159i −0.0242929 0.0242929i
\(134\) −11.3689 −0.982127
\(135\) −21.9649 + 1.95364i −1.89044 + 0.168143i
\(136\) 3.24365 0.278141
\(137\) −9.10365 + 9.10365i −0.777778 + 0.777778i −0.979453 0.201675i \(-0.935362\pi\)
0.201675 + 0.979453i \(0.435362\pi\)
\(138\) −18.0422 + 18.0422i −1.53586 + 1.53586i
\(139\) 12.3301 1.04583 0.522914 0.852385i \(-0.324845\pi\)
0.522914 + 0.852385i \(0.324845\pi\)
\(140\) 2.22728 0.198102i 0.188239 0.0167427i
\(141\) 14.1876 1.19481
\(142\) −4.71214 4.71214i −0.395434 0.395434i
\(143\) 11.8474 + 9.99565i 0.990727 + 0.835878i
\(144\) 6.24365i 0.520304i
\(145\) 8.49921 + 7.11079i 0.705821 + 0.590519i
\(146\) −5.50428 −0.455538
\(147\) 2.14984 2.14984i 0.177316 0.177316i
\(148\) −5.43000 5.43000i −0.446343 0.446343i
\(149\) 5.76190 0.472033 0.236017 0.971749i \(-0.424158\pi\)
0.236017 + 0.971749i \(0.424158\pi\)
\(150\) −14.9631 + 2.68297i −1.22173 + 0.219063i
\(151\) 14.0115i 1.14024i 0.821562 + 0.570120i \(0.193103\pi\)
−0.821562 + 0.570120i \(0.806897\pi\)
\(152\) −0.280159 + 0.280159i −0.0227239 + 0.0227239i
\(153\) −14.3205 + 14.3205i −1.15774 + 1.15774i
\(154\) 3.30477 0.280159i 0.266306 0.0225759i
\(155\) −5.56286 4.65412i −0.446820 0.373828i
\(156\) 14.2095i 1.13767i
\(157\) 5.18890 5.18890i 0.414119 0.414119i −0.469052 0.883171i \(-0.655404\pi\)
0.883171 + 0.469052i \(0.155404\pi\)
\(158\) −9.98302 9.98302i −0.794206 0.794206i
\(159\) 42.6413i 3.38167i
\(160\) −0.198102 2.22728i −0.0156614 0.176082i
\(161\) 8.39234i 0.661409i
\(162\) 7.95652 + 7.95652i 0.625123 + 0.625123i
\(163\) 8.77731 + 8.77731i 0.687492 + 0.687492i 0.961677 0.274185i \(-0.0884081\pi\)
−0.274185 + 0.961677i \(0.588408\pi\)
\(164\) 6.00143 0.468633
\(165\) −22.2101 + 3.88760i −1.72905 + 0.302649i
\(166\) 2.68207 0.208169
\(167\) 7.12630 + 7.12630i 0.551450 + 0.551450i 0.926859 0.375410i \(-0.122498\pi\)
−0.375410 + 0.926859i \(0.622498\pi\)
\(168\) −2.14984 2.14984i −0.165864 0.165864i
\(169\) 8.84302i 0.680232i
\(170\) −4.65412 + 5.56286i −0.356955 + 0.426652i
\(171\) 2.47376i 0.189173i
\(172\) 7.83946 + 7.83946i 0.597753 + 0.597753i
\(173\) 11.6695 11.6695i 0.887216 0.887216i −0.107039 0.994255i \(-0.534137\pi\)
0.994255 + 0.107039i \(0.0341370\pi\)
\(174\) 15.0673i 1.14225i
\(175\) −2.85604 + 4.10403i −0.215897 + 0.310235i
\(176\) −0.280159 3.30477i −0.0211178 0.249106i
\(177\) 26.7700 26.7700i 2.01216 2.01216i
\(178\) 4.14970 4.14970i 0.311033 0.311033i
\(179\) 7.23523i 0.540787i 0.962750 + 0.270393i \(0.0871537\pi\)
−0.962750 + 0.270393i \(0.912846\pi\)
\(180\) 10.7079 + 8.95865i 0.798117 + 0.667738i
\(181\) −13.9173 −1.03446 −0.517232 0.855845i \(-0.673038\pi\)
−0.517232 + 0.855845i \(0.673038\pi\)
\(182\) −3.30477 3.30477i −0.244966 0.244966i
\(183\) 16.9940 16.9940i 1.25624 1.25624i
\(184\) 8.39234 0.618692
\(185\) 17.1037 1.52126i 1.25749 0.111846i
\(186\) 9.86179i 0.723101i
\(187\) −6.93727 + 8.22242i −0.507303 + 0.601283i
\(188\) −3.29969 3.29969i −0.240654 0.240654i
\(189\) 9.86179 0.717340
\(190\) −0.0784891 0.882457i −0.00569420 0.0640202i
\(191\) −1.33603 −0.0966716 −0.0483358 0.998831i \(-0.515392\pi\)
−0.0483358 + 0.998831i \(0.515392\pi\)
\(192\) −2.14984 + 2.14984i −0.155152 + 0.155152i
\(193\) 9.99085 9.99085i 0.719157 0.719157i −0.249275 0.968433i \(-0.580192\pi\)
0.968433 + 0.249275i \(0.0801924\pi\)
\(194\) −4.58721 −0.329343
\(195\) 24.3693 + 20.3884i 1.74512 + 1.46004i
\(196\) −1.00000 −0.0714286
\(197\) 9.91342 + 9.91342i 0.706302 + 0.706302i 0.965756 0.259454i \(-0.0835425\pi\)
−0.259454 + 0.965756i \(0.583542\pi\)
\(198\) 15.8272 + 13.3534i 1.12479 + 0.948988i
\(199\) 8.36429i 0.592929i 0.955044 + 0.296464i \(0.0958076\pi\)
−0.955044 + 0.296464i \(0.904192\pi\)
\(200\) 4.10403 + 2.85604i 0.290198 + 0.201953i
\(201\) −34.5654 −2.43806
\(202\) 2.11079 2.11079i 0.148515 0.148515i
\(203\) −3.50428 3.50428i −0.245952 0.245952i
\(204\) 9.86179 0.690463
\(205\) −8.61110 + 10.2925i −0.601425 + 0.718856i
\(206\) 3.45023i 0.240389i
\(207\) −37.0516 + 37.0516i −2.57526 + 2.57526i
\(208\) −3.30477 + 3.30477i −0.229145 + 0.229145i
\(209\) −0.111000 1.30937i −0.00767805 0.0905707i
\(210\) 6.77167 0.602298i 0.467289 0.0415625i
\(211\) 21.1203i 1.45398i 0.686649 + 0.726990i \(0.259081\pi\)
−0.686649 + 0.726990i \(0.740919\pi\)
\(212\) 9.91730 9.91730i 0.681123 0.681123i
\(213\) −14.3265 14.3265i −0.981635 0.981635i
\(214\) 3.30825i 0.226147i
\(215\) −24.6931 + 2.19630i −1.68405 + 0.149786i
\(216\) 9.86179i 0.671010i
\(217\) 2.29361 + 2.29361i 0.155700 + 0.155700i
\(218\) −6.97334 6.97334i −0.472294 0.472294i
\(219\) −16.7349 −1.13084
\(220\) 6.06967 + 4.26135i 0.409217 + 0.287300i
\(221\) 15.1597 1.01975
\(222\) −16.5090 16.5090i −1.10801 1.10801i
\(223\) 7.59095 + 7.59095i 0.508328 + 0.508328i 0.914013 0.405685i \(-0.132967\pi\)
−0.405685 + 0.914013i \(0.632967\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) −30.7282 + 5.50975i −2.04855 + 0.367317i
\(226\) 3.79480i 0.252427i
\(227\) −18.3263 18.3263i −1.21636 1.21636i −0.968898 0.247462i \(-0.920404\pi\)
−0.247462 0.968898i \(-0.579596\pi\)
\(228\) −0.851778 + 0.851778i −0.0564104 + 0.0564104i
\(229\) 2.02681i 0.133935i 0.997755 + 0.0669676i \(0.0213324\pi\)
−0.997755 + 0.0669676i \(0.978668\pi\)
\(230\) −12.0417 + 14.3929i −0.794005 + 0.949038i
\(231\) 10.0476 0.851778i 0.661085 0.0560429i
\(232\) −3.50428 + 3.50428i −0.230067 + 0.230067i
\(233\) 5.66641 5.66641i 0.371219 0.371219i −0.496702 0.867921i \(-0.665456\pi\)
0.867921 + 0.496702i \(0.165456\pi\)
\(234\) 29.1806i 1.90760i
\(235\) 10.3935 0.924437i 0.677997 0.0603036i
\(236\) −12.4521 −0.810561
\(237\) −30.3517 30.3517i −1.97156 1.97156i
\(238\) 2.29361 2.29361i 0.148672 0.148672i
\(239\) −0.0913582 −0.00590947 −0.00295474 0.999996i \(-0.500941\pi\)
−0.00295474 + 0.999996i \(0.500941\pi\)
\(240\) −0.602298 6.77167i −0.0388782 0.437109i
\(241\) 24.6673i 1.58896i −0.607291 0.794479i \(-0.707744\pi\)
0.607291 0.794479i \(-0.292256\pi\)
\(242\) 8.97654 + 6.35781i 0.577034 + 0.408695i
\(243\) 3.27048 + 3.27048i 0.209801 + 0.209801i
\(244\) −7.90478 −0.506052
\(245\) 1.43484 1.71500i 0.0916687 0.109567i
\(246\) 18.2464 1.16335
\(247\) −1.30937 + 1.30937i −0.0833130 + 0.0833130i
\(248\) 2.29361 2.29361i 0.145644 0.145644i
\(249\) 8.15440 0.516764
\(250\) −10.7867 + 2.94044i −0.682214 + 0.185970i
\(251\) 4.52253 0.285459 0.142730 0.989762i \(-0.454412\pi\)
0.142730 + 0.989762i \(0.454412\pi\)
\(252\) −4.41493 4.41493i −0.278114 0.278114i
\(253\) −17.9489 + 21.2740i −1.12844 + 1.33748i
\(254\) 2.15698i 0.135341i
\(255\) −14.1501 + 16.9130i −0.886114 + 1.05913i
\(256\) 1.00000 0.0625000
\(257\) 4.19603 4.19603i 0.261741 0.261741i −0.564020 0.825761i \(-0.690746\pi\)
0.825761 + 0.564020i \(0.190746\pi\)
\(258\) 23.8346 + 23.8346i 1.48388 + 1.48388i
\(259\) −7.67918 −0.477161
\(260\) −0.925861 10.4095i −0.0574195 0.645570i
\(261\) 30.9423i 1.91528i
\(262\) −8.28016 + 8.28016i −0.511550 + 0.511550i
\(263\) −0.0552305 + 0.0552305i −0.00340566 + 0.00340566i −0.708808 0.705402i \(-0.750767\pi\)
0.705402 + 0.708808i \(0.250767\pi\)
\(264\) −0.851778 10.0476i −0.0524233 0.618388i
\(265\) 2.77842 + 31.2379i 0.170677 + 1.91893i
\(266\) 0.396205i 0.0242929i
\(267\) 12.6165 12.6165i 0.772117 0.772117i
\(268\) 8.03905 + 8.03905i 0.491063 + 0.491063i
\(269\) 12.1268i 0.739387i 0.929154 + 0.369693i \(0.120537\pi\)
−0.929154 + 0.369693i \(0.879463\pi\)
\(270\) 16.9130 + 14.1501i 1.02929 + 0.861148i
\(271\) 29.5438i 1.79466i −0.441361 0.897330i \(-0.645504\pi\)
0.441361 0.897330i \(-0.354496\pi\)
\(272\) −2.29361 2.29361i −0.139070 0.139070i
\(273\) −10.0476 10.0476i −0.608109 0.608109i
\(274\) 12.8745 0.777778
\(275\) −16.0172 + 4.29512i −0.965876 + 0.259006i
\(276\) 25.5156 1.53586
\(277\) −13.8272 13.8272i −0.830796 0.830796i 0.156830 0.987626i \(-0.449873\pi\)
−0.987626 + 0.156830i \(0.949873\pi\)
\(278\) −8.71872 8.71872i −0.522914 0.522914i
\(279\) 20.2522i 1.21247i
\(280\) −1.71500 1.43484i −0.102491 0.0857482i
\(281\) 9.82025i 0.585827i −0.956139 0.292913i \(-0.905375\pi\)
0.956139 0.292913i \(-0.0946248\pi\)
\(282\) −10.0322 10.0322i −0.597406 0.597406i
\(283\) −16.4625 + 16.4625i −0.978592 + 0.978592i −0.999776 0.0211836i \(-0.993257\pi\)
0.0211836 + 0.999776i \(0.493257\pi\)
\(284\) 6.66397i 0.395434i
\(285\) −0.238633 2.68297i −0.0141354 0.158925i
\(286\) −1.30937 15.4453i −0.0774244 0.913303i
\(287\) 4.24365 4.24365i 0.250495 0.250495i
\(288\) −4.41493 + 4.41493i −0.260152 + 0.260152i
\(289\) 6.47874i 0.381102i
\(290\) −0.981756 11.0379i −0.0576507 0.648170i
\(291\) −13.9467 −0.817569
\(292\) 3.89212 + 3.89212i 0.227769 + 0.227769i
\(293\) 0.805207 0.805207i 0.0470407 0.0470407i −0.683195 0.730236i \(-0.739410\pi\)
0.730236 + 0.683195i \(0.239410\pi\)
\(294\) −3.04034 −0.177316
\(295\) 17.8668 21.3553i 1.04024 1.24335i
\(296\) 7.67918i 0.446343i
\(297\) 24.9989 + 21.0916i 1.45058 + 1.22386i
\(298\) −4.07428 4.07428i −0.236017 0.236017i
\(299\) 39.2229 2.26832
\(300\) 12.4776 + 8.68333i 0.720396 + 0.501332i
\(301\) 11.0867 0.639025
\(302\) 9.90762 9.90762i 0.570120 0.570120i
\(303\) 6.41751 6.41751i 0.368676 0.368676i
\(304\) 0.396205 0.0227239
\(305\) 11.3421 13.5567i 0.649447 0.776255i
\(306\) 20.2522 1.15774
\(307\) 20.5089 + 20.5089i 1.17051 + 1.17051i 0.982089 + 0.188416i \(0.0603352\pi\)
0.188416 + 0.982089i \(0.439665\pi\)
\(308\) −2.53493 2.13872i −0.144441 0.121865i
\(309\) 10.4899i 0.596748i
\(310\) 0.642575 + 7.22450i 0.0364958 + 0.410324i
\(311\) 3.03411 0.172049 0.0860243 0.996293i \(-0.472584\pi\)
0.0860243 + 0.996293i \(0.472584\pi\)
\(312\) −10.0476 + 10.0476i −0.568834 + 0.568834i
\(313\) −10.7870 10.7870i −0.609716 0.609716i 0.333155 0.942872i \(-0.391887\pi\)
−0.942872 + 0.333155i \(0.891887\pi\)
\(314\) −7.33821 −0.414119
\(315\) 13.9063 1.23688i 0.783533 0.0696904i
\(316\) 14.1181i 0.794206i
\(317\) 1.99158 1.99158i 0.111858 0.111858i −0.648962 0.760821i \(-0.724797\pi\)
0.760821 + 0.648962i \(0.224797\pi\)
\(318\) 30.1519 30.1519i 1.69084 1.69084i
\(319\) −1.38841 16.3778i −0.0777362 0.916980i
\(320\) −1.43484 + 1.71500i −0.0802101 + 0.0958715i
\(321\) 10.0582i 0.561394i
\(322\) 5.93428 5.93428i 0.330705 0.330705i
\(323\) −0.908738 0.908738i −0.0505635 0.0505635i
\(324\) 11.2522i 0.625123i
\(325\) 19.1808 + 13.3481i 1.06396 + 0.740422i
\(326\) 12.4130i 0.687492i
\(327\) −21.2013 21.2013i −1.17243 1.17243i
\(328\) −4.24365 4.24365i −0.234316 0.234316i
\(329\) −4.66646 −0.257270
\(330\) 18.4538 + 12.9559i 1.01585 + 0.713201i
\(331\) 18.2292 1.00197 0.500985 0.865456i \(-0.332971\pi\)
0.500985 + 0.865456i \(0.332971\pi\)
\(332\) −1.89651 1.89651i −0.104085 0.104085i
\(333\) −33.9030 33.9030i −1.85787 1.85787i
\(334\) 10.0781i 0.551450i
\(335\) −25.3218 + 2.25221i −1.38348 + 0.123052i
\(336\) 3.04034i 0.165864i
\(337\) 12.3955 + 12.3955i 0.675224 + 0.675224i 0.958916 0.283692i \(-0.0915593\pi\)
−0.283692 + 0.958916i \(0.591559\pi\)
\(338\) −6.25296 + 6.25296i −0.340116 + 0.340116i
\(339\) 11.5375i 0.626630i
\(340\) 7.22450 0.642575i 0.391804 0.0348485i
\(341\) 0.908738 + 10.7195i 0.0492109 + 0.580495i
\(342\) −1.74921 + 1.74921i −0.0945867 + 0.0945867i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 11.0867i 0.597753i
\(345\) −36.6108 + 43.7592i −1.97106 + 2.35592i
\(346\) −16.5032 −0.887216
\(347\) −12.2112 12.2112i −0.655530 0.655530i 0.298789 0.954319i \(-0.403417\pi\)
−0.954319 + 0.298789i \(0.903417\pi\)
\(348\) −10.6542 + 10.6542i −0.571125 + 0.571125i
\(349\) 28.1572 1.50722 0.753611 0.657321i \(-0.228310\pi\)
0.753611 + 0.657321i \(0.228310\pi\)
\(350\) 4.92151 0.882457i 0.263066 0.0471693i
\(351\) 46.0906i 2.46013i
\(352\) −2.13872 + 2.53493i −0.113994 + 0.135112i
\(353\) −7.08667 7.08667i −0.377185 0.377185i 0.492900 0.870086i \(-0.335937\pi\)
−0.870086 + 0.492900i \(0.835937\pi\)
\(354\) −37.8585 −2.01216
\(355\) −11.4287 9.56175i −0.606573 0.507485i
\(356\) −5.86857 −0.311033
\(357\) 6.97334 6.97334i 0.369068 0.369068i
\(358\) 5.11608 5.11608i 0.270393 0.270393i
\(359\) −2.73707 −0.144457 −0.0722285 0.997388i \(-0.523011\pi\)
−0.0722285 + 0.997388i \(0.523011\pi\)
\(360\) −1.23688 13.9063i −0.0651894 0.732928i
\(361\) −18.8430 −0.991738
\(362\) 9.84102 + 9.84102i 0.517232 + 0.517232i
\(363\) 27.2917 + 19.3299i 1.43244 + 1.01456i
\(364\) 4.67365i 0.244966i
\(365\) −12.2596 + 1.09041i −0.641694 + 0.0570747i
\(366\) −24.0332 −1.25624
\(367\) −0.607936 + 0.607936i −0.0317340 + 0.0317340i −0.722796 0.691062i \(-0.757143\pi\)
0.691062 + 0.722796i \(0.257143\pi\)
\(368\) −5.93428 5.93428i −0.309346 0.309346i
\(369\) 37.4708 1.95065
\(370\) −13.1698 11.0184i −0.684666 0.572820i
\(371\) 14.0252i 0.728151i
\(372\) 6.97334 6.97334i 0.361551 0.361551i
\(373\) −0.912961 + 0.912961i −0.0472713 + 0.0472713i −0.730347 0.683076i \(-0.760642\pi\)
0.683076 + 0.730347i \(0.260642\pi\)
\(374\) 10.7195 0.908738i 0.554293 0.0469897i
\(375\) −32.7953 + 8.93992i −1.69354 + 0.461656i
\(376\) 4.66646i 0.240654i
\(377\) −16.3778 + 16.3778i −0.843499 + 0.843499i
\(378\) −6.97334 6.97334i −0.358670 0.358670i
\(379\) 4.09747i 0.210473i 0.994447 + 0.105236i \(0.0335599\pi\)
−0.994447 + 0.105236i \(0.966440\pi\)
\(380\) −0.568491 + 0.679492i −0.0291630 + 0.0348572i
\(381\) 6.55794i 0.335973i
\(382\) 0.944714 + 0.944714i 0.0483358 + 0.0483358i
\(383\) −16.3864 16.3864i −0.837304 0.837304i 0.151200 0.988503i \(-0.451686\pi\)
−0.988503 + 0.151200i \(0.951686\pi\)
\(384\) 3.04034 0.155152
\(385\) 7.30513 1.27867i 0.372304 0.0651673i
\(386\) −14.1292 −0.719157
\(387\) 48.9468 + 48.9468i 2.48811 + 2.48811i
\(388\) 3.24365 + 3.24365i 0.164671 + 0.164671i
\(389\) 25.7371i 1.30492i 0.757821 + 0.652462i \(0.226264\pi\)
−0.757821 + 0.652462i \(0.773736\pi\)
\(390\) −2.81493 31.6484i −0.142540 1.60258i
\(391\) 27.2218i 1.37667i
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) −25.1745 + 25.1745i −1.26988 + 1.26988i
\(394\) 14.0197i 0.706302i
\(395\) −24.2126 20.2573i −1.21827 1.01925i
\(396\) −1.74921 20.6338i −0.0879014 1.03689i
\(397\) −7.97079 + 7.97079i −0.400043 + 0.400043i −0.878248 0.478205i \(-0.841287\pi\)
0.478205 + 0.878248i \(0.341287\pi\)
\(398\) 5.91444 5.91444i 0.296464 0.296464i
\(399\) 1.20460i 0.0603052i
\(400\) −0.882457 4.92151i −0.0441229 0.246076i
\(401\) 26.0503 1.30089 0.650446 0.759553i \(-0.274582\pi\)
0.650446 + 0.759553i \(0.274582\pi\)
\(402\) 24.4414 + 24.4414i 1.21903 + 1.21903i
\(403\) 10.7195 10.7195i 0.533977 0.533977i
\(404\) −2.98511 −0.148515
\(405\) 19.2976 + 16.1451i 0.958903 + 0.802259i
\(406\) 4.95580i 0.245952i
\(407\) −19.4662 16.4236i −0.964903 0.814090i
\(408\) −6.97334 6.97334i −0.345232 0.345232i
\(409\) 8.50930 0.420758 0.210379 0.977620i \(-0.432530\pi\)
0.210379 + 0.977620i \(0.432530\pi\)
\(410\) 13.3668 1.18890i 0.660141 0.0587154i
\(411\) 39.1429 1.93077
\(412\) 2.43968 2.43968i 0.120195 0.120195i
\(413\) −8.80495 + 8.80495i −0.433263 + 0.433263i
\(414\) 52.3989 2.57526
\(415\) 5.97371 0.531324i 0.293238 0.0260817i
\(416\) 4.67365 0.229145
\(417\) −26.5079 26.5079i −1.29810 1.29810i
\(418\) −0.847372 + 1.00435i −0.0414463 + 0.0491244i
\(419\) 3.69905i 0.180711i 0.995910 + 0.0903553i \(0.0288003\pi\)
−0.995910 + 0.0903553i \(0.971200\pi\)
\(420\) −5.21418 4.36240i −0.254426 0.212863i
\(421\) −13.8295 −0.674009 −0.337005 0.941503i \(-0.609414\pi\)
−0.337005 + 0.941503i \(0.609414\pi\)
\(422\) 14.9343 14.9343i 0.726990 0.726990i
\(423\) −20.6021 20.6021i −1.00171 1.00171i
\(424\) −14.0252 −0.681123
\(425\) −9.26400 + 13.3120i −0.449370 + 0.645728i
\(426\) 20.2607i 0.981635i
\(427\) −5.58952 + 5.58952i −0.270496 + 0.270496i
\(428\) −2.33929 + 2.33929i −0.113074 + 0.113074i
\(429\) −3.98091 46.9591i −0.192200 2.26721i
\(430\) 19.0137 + 15.9076i 0.916920 + 0.767134i
\(431\) 34.4635i 1.66005i 0.557727 + 0.830024i \(0.311673\pi\)
−0.557727 + 0.830024i \(0.688327\pi\)
\(432\) −6.97334 + 6.97334i −0.335505 + 0.335505i
\(433\) 6.51285 + 6.51285i 0.312987 + 0.312987i 0.846066 0.533078i \(-0.178965\pi\)
−0.533078 + 0.846066i \(0.678965\pi\)
\(434\) 3.24365i 0.155700i
\(435\) −2.98487 33.5591i −0.143114 1.60903i
\(436\) 9.86179i 0.472294i
\(437\) −2.35119 2.35119i −0.112473 0.112473i
\(438\) 11.8333 + 11.8333i 0.565419 + 0.565419i
\(439\) −25.6850 −1.22588 −0.612940 0.790129i \(-0.710013\pi\)
−0.612940 + 0.790129i \(0.710013\pi\)
\(440\) −1.27867 7.30513i −0.0609584 0.348259i
\(441\) −6.24365 −0.297317
\(442\) −10.7195 10.7195i −0.509876 0.509876i
\(443\) 22.1440 + 22.1440i 1.05209 + 1.05209i 0.998566 + 0.0535252i \(0.0170458\pi\)
0.0535252 + 0.998566i \(0.482954\pi\)
\(444\) 23.3473i 1.10801i
\(445\) 8.42047 10.0646i 0.399168 0.477108i
\(446\) 10.7352i 0.508328i
\(447\) −12.3872 12.3872i −0.585894 0.585894i
\(448\) 0.707107 0.707107i 0.0334077 0.0334077i
\(449\) 8.11207i 0.382832i −0.981509 0.191416i \(-0.938692\pi\)
0.981509 0.191416i \(-0.0613080\pi\)
\(450\) 25.6241 + 17.8321i 1.20793 + 0.840615i
\(451\) 19.8333 1.68135i 0.933916 0.0791719i
\(452\) −2.68333 + 2.68333i −0.126213 + 0.126213i
\(453\) 30.1225 30.1225i 1.41528 1.41528i
\(454\) 25.9173i 1.21636i
\(455\) −8.01532 6.70595i −0.375764 0.314380i
\(456\) 1.20460 0.0564104
\(457\) −3.42443 3.42443i −0.160188 0.160188i 0.622462 0.782650i \(-0.286133\pi\)
−0.782650 + 0.622462i \(0.786133\pi\)
\(458\) 1.43317 1.43317i 0.0669676 0.0669676i
\(459\) 31.9882 1.49308
\(460\) 18.6921 1.66254i 0.871522 0.0775165i
\(461\) 12.1649i 0.566578i −0.959035 0.283289i \(-0.908574\pi\)
0.959035 0.283289i \(-0.0914256\pi\)
\(462\) −7.70704 6.50244i −0.358564 0.302521i
\(463\) −10.6249 10.6249i −0.493782 0.493782i 0.415714 0.909496i \(-0.363532\pi\)
−0.909496 + 0.415714i \(0.863532\pi\)
\(464\) 4.95580 0.230067
\(465\) 1.95364 + 21.9649i 0.0905981 + 1.01860i
\(466\) −8.01351 −0.371219
\(467\) 3.74065 3.74065i 0.173097 0.173097i −0.615242 0.788338i \(-0.710942\pi\)
0.788338 + 0.615242i \(0.210942\pi\)
\(468\) −20.6338 + 20.6338i −0.953799 + 0.953799i
\(469\) 11.3689 0.524969
\(470\) −8.00298 6.69563i −0.369150 0.308847i
\(471\) −22.3106 −1.02802
\(472\) 8.80495 + 8.80495i 0.405280 + 0.405280i
\(473\) 28.1039 + 23.7113i 1.29222 + 1.09025i
\(474\) 42.9238i 1.97156i
\(475\) −0.349634 1.94993i −0.0160423 0.0894687i
\(476\) −3.24365 −0.148672
\(477\) 61.9202 61.9202i 2.83513 2.83513i
\(478\) 0.0646000 + 0.0646000i 0.00295474 + 0.00295474i
\(479\) 24.1281 1.10244 0.551220 0.834360i \(-0.314163\pi\)
0.551220 + 0.834360i \(0.314163\pi\)
\(480\) −4.36240 + 5.21418i −0.199116 + 0.237994i
\(481\) 35.8898i 1.63644i
\(482\) −17.4424 + 17.4424i −0.794479 + 0.794479i
\(483\) 18.0422 18.0422i 0.820950 0.820950i
\(484\) −1.85172 10.8430i −0.0841692 0.492865i
\(485\) −10.2170 + 0.908738i −0.463930 + 0.0412637i
\(486\) 4.62516i 0.209801i
\(487\) −12.1610 + 12.1610i −0.551065 + 0.551065i −0.926748 0.375683i \(-0.877408\pi\)
0.375683 + 0.926748i \(0.377408\pi\)
\(488\) 5.58952 + 5.58952i 0.253026 + 0.253026i
\(489\) 37.7397i 1.70665i
\(490\) −2.22728 + 0.198102i −0.100618 + 0.00894935i
\(491\) 5.15042i 0.232435i 0.993224 + 0.116218i \(0.0370770\pi\)
−0.993224 + 0.116218i \(0.962923\pi\)
\(492\) −12.9021 12.9021i −0.581673 0.581673i
\(493\) −11.3667 11.3667i −0.511929 0.511929i
\(494\) 1.85172 0.0833130
\(495\) 37.8969 + 26.6064i 1.70334 + 1.19587i
\(496\) −3.24365 −0.145644
\(497\) 4.71214 + 4.71214i 0.211368 + 0.211368i
\(498\) −5.76603 5.76603i −0.258382 0.258382i
\(499\) 28.5435i 1.27778i −0.769297 0.638891i \(-0.779394\pi\)
0.769297 0.638891i \(-0.220606\pi\)
\(500\) 9.70658 + 5.54818i 0.434092 + 0.248122i
\(501\) 30.6408i 1.36893i
\(502\) −3.19791 3.19791i −0.142730 0.142730i
\(503\) 0.756282 0.756282i 0.0337209 0.0337209i −0.690045 0.723766i \(-0.742409\pi\)
0.723766 + 0.690045i \(0.242409\pi\)
\(504\) 6.24365i 0.278114i
\(505\) 4.28316 5.11946i 0.190598 0.227813i
\(506\) 27.7348 2.35119i 1.23296 0.104523i
\(507\) −19.0111 + 19.0111i −0.844313 + 0.844313i
\(508\) 1.52521 1.52521i 0.0676704 0.0676704i
\(509\) 15.1157i 0.669992i 0.942220 + 0.334996i \(0.108735\pi\)
−0.942220 + 0.334996i \(0.891265\pi\)
\(510\) 21.9649 1.95364i 0.972623 0.0865088i
\(511\) 5.50428 0.243495
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −2.76287 + 2.76287i −0.121984 + 0.121984i
\(514\) −5.93409 −0.261741
\(515\) 0.683499 + 7.68461i 0.0301186 + 0.338625i
\(516\) 33.7072i 1.48388i
\(517\) −11.8291 9.98027i −0.520245 0.438932i
\(518\) 5.43000 + 5.43000i 0.238581 + 0.238581i
\(519\) −50.1752 −2.20245
\(520\) −6.70595 + 8.01532i −0.294075 + 0.351495i
\(521\) 31.0844 1.36183 0.680917 0.732361i \(-0.261581\pi\)
0.680917 + 0.732361i \(0.261581\pi\)
\(522\) −21.8795 + 21.8795i −0.957640 + 0.957640i
\(523\) 11.5361 11.5361i 0.504437 0.504437i −0.408377 0.912813i \(-0.633905\pi\)
0.912813 + 0.408377i \(0.133905\pi\)
\(524\) 11.7099 0.511550
\(525\) 14.9631 2.68297i 0.653041 0.117094i
\(526\) 0.0781078 0.00340566
\(527\) 7.43966 + 7.43966i 0.324077 + 0.324077i
\(528\) −6.50244 + 7.70704i −0.282982 + 0.335406i
\(529\) 47.4315i 2.06224i
\(530\) 20.1239 24.0532i 0.874127 1.04480i
\(531\) −77.7464 −3.37391
\(532\) 0.280159 0.280159i 0.0121464 0.0121464i
\(533\) −19.8333 19.8333i −0.859077 0.859077i
\(534\) −17.8424 −0.772117
\(535\) −0.655372 7.36838i −0.0283342 0.318563i
\(536\) 11.3689i 0.491063i
\(537\) 15.5546 15.5546i 0.671231 0.671231i
\(538\) 8.57497 8.57497i 0.369693 0.369693i
\(539\) −3.30477 + 0.280159i −0.142347 + 0.0120673i
\(540\) −1.95364 21.9649i −0.0840714 0.945220i
\(541\) 35.3282i 1.51888i 0.650579 + 0.759438i \(0.274526\pi\)
−0.650579 + 0.759438i \(0.725474\pi\)
\(542\) −20.8906 + 20.8906i −0.897330 + 0.897330i
\(543\) 29.9200 + 29.9200i 1.28399 + 1.28399i
\(544\) 3.24365i 0.139070i
\(545\) −16.9130 14.1501i −0.724472 0.606124i
\(546\) 14.2095i 0.608109i
\(547\) −15.7186 15.7186i −0.672081 0.672081i 0.286115 0.958195i \(-0.407636\pi\)
−0.958195 + 0.286115i \(0.907636\pi\)
\(548\) −9.10365 9.10365i −0.388889 0.388889i
\(549\) −49.3547 −2.10641
\(550\) 14.3630 + 8.28879i 0.612441 + 0.353435i
\(551\) 1.96351 0.0836484
\(552\) −18.0422 18.0422i −0.767928 0.767928i
\(553\) 9.98302 + 9.98302i 0.424521 + 0.424521i
\(554\) 19.5546i 0.830796i
\(555\) −40.0406 33.4997i −1.69963 1.42198i
\(556\) 12.3301i 0.522914i
\(557\) 9.98234 + 9.98234i 0.422965 + 0.422965i 0.886223 0.463258i \(-0.153320\pi\)
−0.463258 + 0.886223i \(0.653320\pi\)
\(558\) 14.3205 14.3205i 0.606234 0.606234i
\(559\) 51.8152i 2.19155i
\(560\) 0.198102 + 2.22728i 0.00837135 + 0.0941196i
\(561\) 32.5910 2.76287i 1.37599 0.116648i
\(562\) −6.94396 + 6.94396i −0.292913 + 0.292913i
\(563\) −14.4920 + 14.4920i −0.610764 + 0.610764i −0.943145 0.332381i \(-0.892148\pi\)
0.332381 + 0.943145i \(0.392148\pi\)
\(564\) 14.1876i 0.597406i
\(565\) −0.751760 8.45207i −0.0316268 0.355581i
\(566\) 23.2814 0.978592
\(567\) −7.95652 7.95652i −0.334142 0.334142i
\(568\) 4.71214 4.71214i 0.197717 0.197717i
\(569\) −22.6568 −0.949824 −0.474912 0.880033i \(-0.657520\pi\)
−0.474912 + 0.880033i \(0.657520\pi\)
\(570\) −1.72840 + 2.06588i −0.0723949 + 0.0865303i
\(571\) 18.4539i 0.772272i 0.922442 + 0.386136i \(0.126190\pi\)
−0.922442 + 0.386136i \(0.873810\pi\)
\(572\) −9.99565 + 11.8474i −0.417939 + 0.495364i
\(573\) 2.87225 + 2.87225i 0.119990 + 0.119990i
\(574\) −6.00143 −0.250495
\(575\) −23.9689 + 34.4424i −0.999572 + 1.43635i
\(576\) 6.24365 0.260152
\(577\) −12.6833 + 12.6833i −0.528014 + 0.528014i −0.919980 0.391966i \(-0.871795\pi\)
0.391966 + 0.919980i \(0.371795\pi\)
\(578\) −4.58116 + 4.58116i −0.190551 + 0.190551i
\(579\) −42.9575 −1.78525
\(580\) −7.11079 + 8.49921i −0.295260 + 0.352910i
\(581\) −2.68207 −0.111271
\(582\) 9.86179 + 9.86179i 0.408784 + 0.408784i
\(583\) 29.9960 35.5528i 1.24231 1.47245i
\(584\) 5.50428i 0.227769i
\(585\) −5.78075 64.9933i −0.239005 2.68714i
\(586\) −1.13873 −0.0470407
\(587\) 18.6007 18.6007i 0.767731 0.767731i −0.209975 0.977707i \(-0.567338\pi\)
0.977707 + 0.209975i \(0.0673384\pi\)
\(588\) 2.14984 + 2.14984i 0.0886580 + 0.0886580i
\(589\) −1.28515 −0.0529537
\(590\) −27.7342 + 2.46679i −1.14180 + 0.101556i
\(591\) 42.6246i 1.75334i
\(592\) 5.43000 5.43000i 0.223172 0.223172i
\(593\) −33.5426 + 33.5426i −1.37743 + 1.37743i −0.528486 + 0.848942i \(0.677240\pi\)
−0.848942 + 0.528486i \(0.822760\pi\)
\(594\) −2.76287 32.5910i −0.113362 1.33722i
\(595\) 4.65412 5.56286i 0.190801 0.228055i
\(596\) 5.76190i 0.236017i
\(597\) 17.9819 17.9819i 0.735950 0.735950i
\(598\) −27.7348 27.7348i −1.13416 1.13416i
\(599\) 17.9354i 0.732821i −0.930453 0.366410i \(-0.880587\pi\)
0.930453 0.366410i \(-0.119413\pi\)
\(600\) −2.68297 14.9631i −0.109532 0.610864i
\(601\) 9.42764i 0.384562i 0.981340 + 0.192281i \(0.0615884\pi\)
−0.981340 + 0.192281i \(0.938412\pi\)
\(602\) −7.83946 7.83946i −0.319513 0.319513i
\(603\) 50.1930 + 50.1930i 2.04402 + 2.04402i
\(604\) −14.0115 −0.570120
\(605\) 21.2527 + 12.3823i 0.864046 + 0.503413i
\(606\) −9.07573 −0.368676
\(607\) −0.368589 0.368589i −0.0149606 0.0149606i 0.699587 0.714548i \(-0.253367\pi\)
−0.714548 + 0.699587i \(0.753367\pi\)
\(608\) −0.280159 0.280159i −0.0113619 0.0113619i
\(609\) 15.0673i 0.610558i
\(610\) −17.6061 + 1.56596i −0.712851 + 0.0634037i
\(611\) 21.8094i 0.882314i
\(612\) −14.3205 14.3205i −0.578871 0.578871i
\(613\) −6.75253 + 6.75253i −0.272732 + 0.272732i −0.830199 0.557467i \(-0.811773\pi\)
0.557467 + 0.830199i \(0.311773\pi\)
\(614\) 29.0040i 1.17051i
\(615\) 40.6397 3.61465i 1.63875 0.145757i
\(616\) 0.280159 + 3.30477i 0.0112879 + 0.133153i
\(617\) 6.80159 6.80159i 0.273822 0.273822i −0.556815 0.830637i \(-0.687977\pi\)
0.830637 + 0.556815i \(0.187977\pi\)
\(618\) 7.41746 7.41746i 0.298374 0.298374i
\(619\) 13.1025i 0.526635i −0.964709 0.263318i \(-0.915183\pi\)
0.964709 0.263318i \(-0.0848168\pi\)
\(620\) 4.65412 5.56286i 0.186914 0.223410i
\(621\) 82.7635 3.32119
\(622\) −2.14544 2.14544i −0.0860243 0.0860243i
\(623\) −4.14970 + 4.14970i −0.166254 + 0.166254i
\(624\) 14.2095 0.568834
\(625\) −23.4425 + 8.68604i −0.937702 + 0.347442i
\(626\) 15.2551i 0.609716i
\(627\) −2.57630 + 3.05356i −0.102887 + 0.121948i
\(628\) 5.18890 + 5.18890i 0.207060 + 0.207060i
\(629\) −24.9086 −0.993170
\(630\) −10.7079 8.95865i −0.426612 0.356921i
\(631\) −48.4453 −1.92857 −0.964287 0.264858i \(-0.914675\pi\)
−0.964287 + 0.264858i \(0.914675\pi\)
\(632\) 9.98302 9.98302i 0.397103 0.397103i
\(633\) 45.4053 45.4053i 1.80470 1.80470i
\(634\) −2.81652 −0.111858
\(635\) 0.427302 + 4.80418i 0.0169570 + 0.190648i
\(636\) −42.6413 −1.69084
\(637\) 3.30477 + 3.30477i 0.130940 + 0.130940i
\(638\) −10.5991 + 12.5626i −0.419622 + 0.497358i
\(639\) 41.6075i 1.64597i
\(640\) 2.22728 0.198102i 0.0880408 0.00783068i
\(641\) 18.5376 0.732192 0.366096 0.930577i \(-0.380694\pi\)
0.366096 + 0.930577i \(0.380694\pi\)
\(642\) −7.11222 + 7.11222i −0.280697 + 0.280697i
\(643\) 24.1330 + 24.1330i 0.951713 + 0.951713i 0.998887 0.0471738i \(-0.0150215\pi\)
−0.0471738 + 0.998887i \(0.515021\pi\)
\(644\) −8.39234 −0.330705
\(645\) 57.8079 + 48.3645i 2.27618 + 1.90435i
\(646\) 1.28515i 0.0505635i
\(647\) −26.8627 + 26.8627i −1.05608 + 1.05608i −0.0577513 + 0.998331i \(0.518393\pi\)
−0.998331 + 0.0577513i \(0.981607\pi\)
\(648\) −7.95652 + 7.95652i −0.312561 + 0.312561i
\(649\) −41.1513 + 3.48856i −1.61533 + 0.136938i
\(650\) −4.12430 23.0014i −0.161768 0.902190i
\(651\) 9.86179i 0.386514i
\(652\) −8.77731 + 8.77731i −0.343746 + 0.343746i
\(653\) −9.03668 9.03668i −0.353632 0.353632i 0.507827 0.861459i \(-0.330449\pi\)
−0.861459 + 0.507827i \(0.830449\pi\)
\(654\) 29.9832i 1.17243i
\(655\) −16.8019 + 20.0825i −0.656504 + 0.784689i
\(656\) 6.00143i 0.234316i
\(657\) 24.3010 + 24.3010i 0.948072 + 0.948072i
\(658\) 3.29969 + 3.29969i 0.128635 + 0.128635i
\(659\) 13.8288 0.538693 0.269346 0.963043i \(-0.413192\pi\)
0.269346 + 0.963043i \(0.413192\pi\)
\(660\) −3.88760 22.2101i −0.151325 0.864526i
\(661\) 15.8833 0.617790 0.308895 0.951096i \(-0.400041\pi\)
0.308895 + 0.951096i \(0.400041\pi\)
\(662\) −12.8900 12.8900i −0.500985 0.500985i
\(663\) −32.5910 32.5910i −1.26573 1.26573i
\(664\) 2.68207i 0.104085i
\(665\) 0.0784891 + 0.882457i 0.00304368 + 0.0342202i
\(666\) 47.9461i 1.85787i
\(667\) −29.4091 29.4091i −1.13873 1.13873i
\(668\) −7.12630 + 7.12630i −0.275725 + 0.275725i
\(669\) 32.6387i 1.26189i
\(670\) 19.4977 + 16.3126i 0.753263 + 0.630212i
\(671\) −26.1235 + 2.21460i −1.00849 + 0.0854935i
\(672\) 2.14984 2.14984i 0.0829320 0.0829320i
\(673\) 28.4404 28.4404i 1.09630 1.09630i 0.101457 0.994840i \(-0.467649\pi\)
0.994840 0.101457i \(-0.0323506\pi\)
\(674\) 17.5298i 0.675224i
\(675\) 40.4730 + 28.1657i 1.55781 + 1.08410i
\(676\) 8.84302 0.340116
\(677\) −7.22013 7.22013i −0.277492 0.277492i 0.554615 0.832107i \(-0.312866\pi\)
−0.832107 + 0.554615i \(0.812866\pi\)
\(678\) −8.15823 + 8.15823i −0.313315 + 0.313315i
\(679\) 4.58721 0.176041
\(680\) −5.56286 4.65412i −0.213326 0.178478i
\(681\) 78.7973i 3.01952i
\(682\) 6.93727 8.22242i 0.265642 0.314853i
\(683\) 0.553161 + 0.553161i 0.0211661 + 0.0211661i 0.717611 0.696445i \(-0.245236\pi\)
−0.696445 + 0.717611i \(0.745236\pi\)
\(684\) 2.47376 0.0945867
\(685\) 28.6751 2.55047i 1.09562 0.0974485i
\(686\) 1.00000 0.0381802
\(687\) 4.35732 4.35732i 0.166242 0.166242i
\(688\) −7.83946 + 7.83946i −0.298877 + 0.298877i
\(689\) −65.5488 −2.49721
\(690\) 56.8302 5.05469i 2.16349 0.192429i
\(691\) −37.0102 −1.40793 −0.703966 0.710233i \(-0.748589\pi\)
−0.703966 + 0.710233i \(0.748589\pi\)
\(692\) 11.6695 + 11.6695i 0.443608 + 0.443608i
\(693\) −15.8272 13.3534i −0.601226 0.507255i
\(694\) 17.2692i 0.655530i
\(695\) −21.1462 17.6918i −0.802121 0.671088i
\(696\) 15.0673 0.571125
\(697\) 13.7649 13.7649i 0.521383 0.521383i
\(698\) −19.9102 19.9102i −0.753611 0.753611i
\(699\) −24.3638 −0.921522
\(700\) −4.10403 2.85604i −0.155118 0.107948i
\(701\) 17.0518i 0.644038i 0.946733 + 0.322019i \(0.104361\pi\)
−0.946733 + 0.322019i \(0.895639\pi\)
\(702\) −32.5910 + 32.5910i −1.23007 + 1.23007i
\(703\) 2.15139 2.15139i 0.0811413 0.0811413i
\(704\) 3.30477 0.280159i 0.124553 0.0105589i
\(705\) −24.3318 20.3570i −0.916388 0.766688i
\(706\) 10.0221i 0.377185i
\(707\) −2.11079 + 2.11079i −0.0793844 + 0.0793844i
\(708\) 26.7700 + 26.7700i 1.00608 + 1.00608i
\(709\) 49.0505i 1.84213i 0.389410 + 0.921065i \(0.372679\pi\)
−0.389410 + 0.921065i \(0.627321\pi\)
\(710\) 1.32015 + 14.8425i 0.0495443 + 0.557029i
\(711\) 88.1486i 3.30583i
\(712\) 4.14970 + 4.14970i 0.155517 + 0.155517i
\(713\) 19.2487 + 19.2487i 0.720871 + 0.720871i
\(714\) −9.86179 −0.369068
\(715\) −5.97608 34.1417i −0.223493 1.27683i
\(716\) −7.23523 −0.270393
\(717\) 0.196406 + 0.196406i 0.00733491 + 0.00733491i
\(718\) 1.93540 + 1.93540i 0.0722285 + 0.0722285i
\(719\) 30.3303i 1.13113i −0.824704 0.565565i \(-0.808658\pi\)
0.824704 0.565565i \(-0.191342\pi\)
\(720\) −8.95865 + 10.7079i −0.333869 + 0.399059i
\(721\) 3.45023i 0.128493i
\(722\) 13.3240 + 13.3240i 0.495869 + 0.495869i
\(723\) −53.0308 + 53.0308i −1.97224 + 1.97224i
\(724\) 13.9173i 0.517232i
\(725\) −4.37328 24.3900i −0.162420 0.905823i
\(726\) −5.62986 32.9664i −0.208944 1.22350i
\(727\) −17.5774 + 17.5774i −0.651911 + 0.651911i −0.953453 0.301542i \(-0.902499\pi\)
0.301542 + 0.953453i \(0.402499\pi\)
\(728\) 3.30477 3.30477i 0.122483 0.122483i
\(729\) 19.6946i 0.729430i
\(730\) 9.43985 + 7.89777i 0.349384 + 0.292310i
\(731\) 35.9613 1.33008
\(732\) 16.9940 + 16.9940i 0.628118 + 0.628118i
\(733\) 13.4698 13.4698i 0.497519 0.497519i −0.413146 0.910665i \(-0.635570\pi\)
0.910665 + 0.413146i \(0.135570\pi\)
\(734\) 0.859751 0.0317340
\(735\) −6.77167 + 0.602298i −0.249777 + 0.0222161i
\(736\) 8.39234i 0.309346i
\(737\) 28.8194 + 24.3150i 1.06158 + 0.895655i
\(738\) −26.4959 26.4959i −0.975326 0.975326i
\(739\) 40.8681 1.50336 0.751678 0.659530i \(-0.229245\pi\)
0.751678 + 0.659530i \(0.229245\pi\)
\(740\) 1.52126 + 17.1037i 0.0559228 + 0.628743i
\(741\) 5.62986 0.206818
\(742\) −9.91730 + 9.91730i −0.364076 + 0.364076i
\(743\) −25.1350 + 25.1350i −0.922112 + 0.922112i −0.997179 0.0750665i \(-0.976083\pi\)
0.0750665 + 0.997179i \(0.476083\pi\)
\(744\) −9.86179 −0.361551
\(745\) −9.88167 8.26742i −0.362036 0.302895i
\(746\) 1.29112 0.0472713
\(747\) −11.8411 11.8411i −0.433245 0.433245i
\(748\) −8.22242 6.93727i −0.300641 0.253652i
\(749\) 3.30825i 0.120881i
\(750\) 29.5113 + 16.8683i 1.07760 + 0.615944i
\(751\) 14.9041 0.543860 0.271930 0.962317i \(-0.412338\pi\)
0.271930 + 0.962317i \(0.412338\pi\)
\(752\) 3.29969 3.29969i 0.120327 0.120327i
\(753\) −9.72272 9.72272i −0.354316 0.354316i
\(754\) 23.1617 0.843499
\(755\) 20.1043 24.0297i 0.731670 0.874531i
\(756\) 9.86179i 0.358670i
\(757\) −33.1370 + 33.1370i −1.20438 + 1.20438i −0.231565 + 0.972819i \(0.574385\pi\)
−0.972819 + 0.231565i \(0.925615\pi\)
\(758\) 2.89735 2.89735i 0.105236 0.105236i
\(759\) 84.3231 7.14841i 3.06073 0.259471i
\(760\) 0.882457 0.0784891i 0.0320101 0.00284710i
\(761\) 35.8947i 1.30118i 0.759428 + 0.650592i \(0.225479\pi\)
−0.759428 + 0.650592i \(0.774521\pi\)
\(762\) 4.63716 4.63716i 0.167987 0.167987i
\(763\) 6.97334 + 6.97334i 0.252452 + 0.252452i
\(764\) 1.33603i 0.0483358i
\(765\) 45.1073 4.01201i 1.63086 0.145055i
\(766\) 23.1738i 0.837304i
\(767\) 41.1513 + 41.1513i 1.48589 + 1.48589i
\(768\) −2.14984 2.14984i −0.0775758 0.0775758i
\(769\) 23.3132 0.840696 0.420348 0.907363i \(-0.361908\pi\)
0.420348 + 0.907363i \(0.361908\pi\)
\(770\) −6.06967 4.26135i −0.218736 0.153568i
\(771\) −18.0416 −0.649753
\(772\) 9.99085 + 9.99085i 0.359579 + 0.359579i
\(773\) −9.24967 9.24967i −0.332687 0.332687i 0.520919 0.853606i \(-0.325589\pi\)
−0.853606 + 0.520919i \(0.825589\pi\)
\(774\) 69.2213i 2.48811i
\(775\) 2.86238 + 15.9637i 0.102820 + 0.573432i
\(776\) 4.58721i 0.164671i
\(777\) 16.5090 + 16.5090i 0.592258 + 0.592258i
\(778\) 18.1989 18.1989i 0.652462 0.652462i
\(779\) 2.37779i 0.0851933i
\(780\) −20.3884 + 24.3693i −0.730020 + 0.872560i
\(781\) 1.86697 + 22.0229i 0.0668055 + 0.788041i
\(782\) 19.2487 19.2487i 0.688334 0.688334i
\(783\) −34.5585 + 34.5585i −1.23502 + 1.23502i
\(784\) 1.00000i 0.0357143i
\(785\) −16.3442 + 1.45372i −0.583350 + 0.0518854i
\(786\) 35.6021 1.26988
\(787\) 38.5215 + 38.5215i 1.37314 + 1.37314i 0.855745 + 0.517398i \(0.173099\pi\)
0.517398 + 0.855745i \(0.326901\pi\)
\(788\) −9.91342 + 9.91342i −0.353151 + 0.353151i
\(789\) 0.237474 0.00845430
\(790\) 2.79683 + 31.4449i 0.0995068 + 1.11876i
\(791\) 3.79480i 0.134928i
\(792\) −13.3534 + 15.8272i −0.474494 + 0.562395i
\(793\) 26.1235 + 26.1235i 0.927672 + 0.927672i
\(794\) 11.2724 0.400043
\(795\) 61.1835 73.1298i 2.16996 2.59365i
\(796\) −8.36429 −0.296464
\(797\) 20.0195 20.0195i 0.709128 0.709128i −0.257224 0.966352i \(-0.582808\pi\)
0.966352 + 0.257224i \(0.0828078\pi\)
\(798\) 0.851778 0.851778i 0.0301526 0.0301526i
\(799\) −15.1364 −0.535486
\(800\) −2.85604 + 4.10403i −0.100976 + 0.145099i
\(801\) −36.6413 −1.29466
\(802\) −18.4204 18.4204i −0.650446 0.650446i
\(803\) 13.9530 + 11.7721i 0.492389 + 0.415430i
\(804\) 34.5654i 1.21903i
\(805\) 12.0417 14.3929i 0.424414 0.507282i
\(806\) −15.1597 −0.533977
\(807\) 26.0708 26.0708i 0.917736 0.917736i
\(808\) 2.11079 + 2.11079i 0.0742573 + 0.0742573i
\(809\) 19.2982 0.678488 0.339244 0.940698i \(-0.389829\pi\)
0.339244 + 0.940698i \(0.389829\pi\)
\(810\) −2.22909 25.0618i −0.0783222 0.880581i
\(811\) 37.9101i 1.33120i 0.746307 + 0.665602i \(0.231825\pi\)
−0.746307 + 0.665602i \(0.768175\pi\)
\(812\) 3.50428 3.50428i 0.122976 0.122976i
\(813\) −63.5146 + 63.5146i −2.22755 + 2.22755i
\(814\) 2.15139 + 25.3779i 0.0754063 + 0.889496i
\(815\) −2.45904 27.6471i −0.0861365 0.968437i
\(816\) 9.86179i 0.345232i
\(817\) −3.10603 + 3.10603i −0.108666 + 0.108666i
\(818\) −6.01698 6.01698i −0.210379 0.210379i
\(819\) 29.1806i 1.01965i
\(820\) −10.2925 8.61110i −0.359428 0.300713i
\(821\) 46.0769i 1.60809i −0.594566 0.804047i \(-0.702676\pi\)
0.594566 0.804047i \(-0.297324\pi\)
\(822\) −27.6782 27.6782i −0.965387 0.965387i
\(823\) −4.86619 4.86619i −0.169625 0.169625i 0.617190 0.786814i \(-0.288271\pi\)
−0.786814 + 0.617190i \(0.788271\pi\)
\(824\) −3.45023 −0.120195
\(825\) 43.6684 + 25.2007i 1.52034 + 0.877376i
\(826\) 12.4521 0.433263
\(827\) −14.7761 14.7761i −0.513814 0.513814i 0.401879 0.915693i \(-0.368357\pi\)
−0.915693 + 0.401879i \(0.868357\pi\)
\(828\) −37.0516 37.0516i −1.28763 1.28763i
\(829\) 18.8528i 0.654786i −0.944888 0.327393i \(-0.893830\pi\)
0.944888 0.327393i \(-0.106170\pi\)
\(830\) −4.59975 3.84835i −0.159660 0.133578i
\(831\) 59.4526i 2.06239i
\(832\) −3.30477 3.30477i −0.114572 0.114572i
\(833\) −2.29361 + 2.29361i −0.0794688 + 0.0794688i
\(834\) 37.4878i 1.29810i
\(835\) −1.99650 22.4467i −0.0690916 0.776801i
\(836\) 1.30937 0.111000i 0.0452854 0.00383903i
\(837\) 22.6191 22.6191i 0.781829 0.781829i
\(838\) 2.61563 2.61563i 0.0903553 0.0903553i
\(839\) 47.8316i 1.65133i −0.564160 0.825665i \(-0.690800\pi\)
0.564160 0.825665i \(-0.309200\pi\)
\(840\) 0.602298 + 6.77167i 0.0207813 + 0.233645i
\(841\) −4.44002 −0.153104
\(842\) 9.77894 + 9.77894i 0.337005 + 0.337005i
\(843\) −21.1120 + 21.1120i −0.727136 + 0.727136i
\(844\) −21.1203 −0.726990
\(845\) −12.6883 + 15.1658i −0.436492 + 0.521719i
\(846\) 29.1357i 1.00171i
\(847\) −8.97654 6.35781i −0.308438 0.218457i
\(848\) 9.91730 + 9.91730i 0.340562 + 0.340562i
\(849\) 70.7834 2.42928
\(850\) 15.9637 2.86238i 0.547549 0.0981789i
\(851\) −64.4463 −2.20919
\(852\) 14.3265 14.3265i 0.490818 0.490818i
\(853\) −29.2794 + 29.2794i −1.00251 + 1.00251i −0.00251044 + 0.999997i \(0.500799\pi\)
−0.999997 + 0.00251044i \(0.999201\pi\)
\(854\) 7.90478 0.270496
\(855\) −3.54946 + 4.24251i −0.121389 + 0.145091i
\(856\) 3.30825 0.113074
\(857\) −6.57238 6.57238i −0.224508 0.224508i 0.585886 0.810394i \(-0.300747\pi\)
−0.810394 + 0.585886i \(0.800747\pi\)
\(858\) −30.3901 + 36.0200i −1.03750 + 1.22970i
\(859\) 16.3959i 0.559421i 0.960084 + 0.279710i \(0.0902384\pi\)
−0.960084 + 0.279710i \(0.909762\pi\)
\(860\) −2.19630 24.6931i −0.0748931 0.842027i
\(861\) −18.2464 −0.621834
\(862\) 24.3694 24.3694i 0.830024 0.830024i
\(863\) 14.5603 + 14.5603i 0.495639 + 0.495639i 0.910077 0.414438i \(-0.136022\pi\)
−0.414438 + 0.910077i \(0.636022\pi\)
\(864\) 9.86179 0.335505
\(865\) −36.7571 + 3.26932i −1.24978 + 0.111160i
\(866\) 9.21055i 0.312987i
\(867\) −13.9283 + 13.9283i −0.473029 + 0.473029i
\(868\) −2.29361 + 2.29361i −0.0778501 + 0.0778501i
\(869\) 3.95532 + 46.6571i 0.134175 + 1.58274i
\(870\) −21.6192 + 25.8405i −0.732960 + 0.876073i
\(871\) 53.1345i 1.80039i
\(872\) 6.97334 6.97334i 0.236147 0.236147i
\(873\) 20.2522 + 20.2522i 0.685434 + 0.685434i
\(874\) 3.32509i 0.112473i
\(875\) 10.7867 2.94044i 0.364658 0.0994049i
\(876\) 16.7349i 0.565419i
\(877\) −19.8407 19.8407i −0.669974 0.669974i 0.287736 0.957710i \(-0.407098\pi\)
−0.957710 + 0.287736i \(0.907098\pi\)
\(878\) 18.1621 + 18.1621i 0.612940 + 0.612940i
\(879\) −3.46214 −0.116775
\(880\) −4.26135 + 6.06967i −0.143650 + 0.204609i
\(881\) −6.16569 −0.207727 −0.103864 0.994592i \(-0.533121\pi\)
−0.103864 + 0.994592i \(0.533121\pi\)
\(882\) 4.41493 + 4.41493i 0.148658 + 0.148658i
\(883\) 13.6906 + 13.6906i 0.460727 + 0.460727i 0.898894 0.438167i \(-0.144372\pi\)
−0.438167 + 0.898894i \(0.644372\pi\)
\(884\) 15.1597i 0.509876i
\(885\) −84.3213 + 7.49986i −2.83443 + 0.252105i
\(886\) 31.3163i 1.05209i
\(887\) 17.5547 + 17.5547i 0.589428 + 0.589428i 0.937476 0.348049i \(-0.113156\pi\)
−0.348049 + 0.937476i \(0.613156\pi\)
\(888\) 16.5090 16.5090i 0.554007 0.554007i
\(889\) 2.15698i 0.0723427i
\(890\) −13.0709 + 1.16258i −0.438138 + 0.0389697i
\(891\) −3.15241 37.1860i −0.105610 1.24578i
\(892\) −7.59095 + 7.59095i −0.254164 + 0.254164i
\(893\) 1.30735 1.30735i 0.0437488 0.0437488i
\(894\) 17.5181i 0.585894i
\(895\) 10.3814 12.4084i 0.347012 0.414768i
\(896\) −1.00000 −0.0334077
\(897\) −84.3231 84.3231i −2.81547 2.81547i
\(898\) −5.73610 + 5.73610i −0.191416 + 0.191416i
\(899\) −16.0749 −0.536128
\(900\) −5.50975 30.7282i −0.183658 1.02427i
\(901\) 45.4928i 1.51558i
\(902\) −15.2132 12.8354i −0.506544 0.427372i
\(903\) −23.8346 23.8346i −0.793166 0.793166i
\(904\) 3.79480 0.126213
\(905\) 23.8682 + 19.9691i 0.793405 + 0.663796i
\(906\) −42.5997 −1.41528
\(907\) 28.1124 28.1124i 0.933456 0.933456i −0.0644643 0.997920i \(-0.520534\pi\)
0.997920 + 0.0644643i \(0.0205339\pi\)
\(908\) 18.3263 18.3263i 0.608180 0.608180i
\(909\) −18.6380 −0.618182
\(910\) 0.925861 + 10.4095i 0.0306920 + 0.345072i
\(911\) 37.3644 1.23794 0.618969 0.785415i \(-0.287550\pi\)
0.618969 + 0.785415i \(0.287550\pi\)
\(912\) −0.851778 0.851778i −0.0282052 0.0282052i
\(913\) −6.79886 5.73621i −0.225009 0.189841i
\(914\) 4.84288i 0.160188i
\(915\) −53.5286 + 4.76103i −1.76960 + 0.157395i
\(916\) −2.02681 −0.0669676
\(917\) 8.28016 8.28016i 0.273435 0.273435i
\(918\) −22.6191 22.6191i −0.746540 0.746540i
\(919\) −24.3864 −0.804433 −0.402217 0.915544i \(-0.631760\pi\)
−0.402217 + 0.915544i \(0.631760\pi\)
\(920\) −14.3929 12.0417i −0.474519 0.397003i
\(921\) 88.1819i 2.90569i
\(922\) −8.60192 + 8.60192i −0.283289 + 0.283289i
\(923\) 22.0229 22.0229i 0.724893 0.724893i
\(924\) 0.851778 + 10.0476i 0.0280214 + 0.330542i
\(925\) −31.5156 21.9321i −1.03623 0.721122i
\(926\) 15.0259i 0.493782i
\(927\) 15.2325 15.2325i 0.500302 0.500302i
\(928\) −3.50428 3.50428i −0.115034 0.115034i
\(929\) 27.2794i 0.895007i −0.894282 0.447504i \(-0.852313\pi\)
0.894282 0.447504i \(-0.147687\pi\)
\(930\) 14.1501 16.9130i 0.464000 0.554598i
\(931\) 0.396205i 0.0129851i
\(932\) 5.66641 + 5.66641i 0.185609 + 0.185609i
\(933\) −6.52286 6.52286i −0.213549 0.213549i
\(934\) −5.29008 −0.173097
\(935\) 23.6953 4.14757i 0.774919 0.135640i
\(936\) 29.1806 0.953799
\(937\) 16.1087 + 16.1087i 0.526248 + 0.526248i 0.919452 0.393203i \(-0.128633\pi\)
−0.393203 + 0.919452i \(0.628633\pi\)
\(938\) −8.03905 8.03905i −0.262484 0.262484i
\(939\) 46.3807i 1.51358i
\(940\) 0.924437 + 10.3935i 0.0301518 + 0.338998i
\(941\) 3.51397i 0.114552i 0.998358 + 0.0572761i \(0.0182415\pi\)
−0.998358 + 0.0572761i \(0.981758\pi\)
\(942\) 15.7760 + 15.7760i 0.514010 + 0.514010i
\(943\) 35.6142 35.6142i 1.15976 1.15976i
\(944\) 12.4521i 0.405280i
\(945\) −16.9130 14.1501i −0.550179 0.460303i
\(946\) −3.10603 36.6389i −0.100986 1.19123i
\(947\) 20.6556 20.6556i 0.671215 0.671215i −0.286781 0.957996i \(-0.592585\pi\)
0.957996 + 0.286781i \(0.0925852\pi\)
\(948\) 30.3517 30.3517i 0.985779 0.985779i
\(949\) 25.7251i 0.835072i
\(950\) −1.13158 + 1.62603i −0.0367132 + 0.0527555i
\(951\) −8.56318 −0.277680
\(952\) 2.29361 + 2.29361i 0.0743362 + 0.0743362i
\(953\) 1.88351 1.88351i 0.0610128 0.0610128i −0.675942 0.736955i \(-0.736263\pi\)
0.736955 + 0.675942i \(0.236263\pi\)
\(954\) −87.5683 −2.83513
\(955\) 2.29129 + 1.91699i 0.0741444 + 0.0620323i
\(956\) 0.0913582i 0.00295474i
\(957\) −32.2248 + 38.1946i −1.04168 + 1.23465i
\(958\) −17.0611 17.0611i −0.551220 0.551220i
\(959\) −12.8745 −0.415740
\(960\) 6.77167 0.602298i 0.218555 0.0194391i
\(961\) −20.4787 −0.660604
\(962\) 25.3779 25.3779i 0.818218 0.818218i
\(963\) −14.6057 + 14.6057i −0.470662 + 0.470662i
\(964\) 24.6673 0.794479
\(965\) −31.4696 + 2.79903i −1.01304 + 0.0901039i
\(966\) −25.5156 −0.820950
\(967\) −6.65882 6.65882i −0.214133 0.214133i 0.591887 0.806021i \(-0.298383\pi\)
−0.806021 + 0.591887i \(0.798383\pi\)
\(968\) −6.35781 + 8.97654i −0.204348 + 0.288517i
\(969\) 3.90729i 0.125520i
\(970\) 7.86708 + 6.58193i 0.252597 + 0.211333i
\(971\) −3.41873 −0.109712 −0.0548561 0.998494i \(-0.517470\pi\)
−0.0548561 + 0.998494i \(0.517470\pi\)
\(972\) −3.27048 + 3.27048i −0.104901 + 0.104901i
\(973\) 8.71872 + 8.71872i 0.279509 + 0.279509i
\(974\) 17.1982 0.551065
\(975\) −12.5393 69.9321i −0.401577 2.23962i
\(976\) 7.90478i 0.253026i
\(977\) 15.4705 15.4705i 0.494944 0.494944i −0.414916 0.909860i \(-0.636189\pi\)
0.909860 + 0.414916i \(0.136189\pi\)
\(978\) −26.6860 + 26.6860i −0.853323 + 0.853323i
\(979\) −19.3943 + 1.64413i −0.619844 + 0.0525467i
\(980\) 1.71500 + 1.43484i 0.0547837 + 0.0458343i
\(981\) 61.5736i 1.96589i
\(982\) 3.64190 3.64190i 0.116218 0.116218i
\(983\) 5.78699 + 5.78699i 0.184576 + 0.184576i 0.793347 0.608770i \(-0.208337\pi\)
−0.608770 + 0.793347i \(0.708337\pi\)
\(984\) 18.2464i 0.581673i
\(985\) −2.77733 31.2257i −0.0884932 0.994934i
\(986\) 16.0749i 0.511929i
\(987\) 10.0322 + 10.0322i 0.319327 + 0.319327i
\(988\) −1.30937 1.30937i −0.0416565 0.0416565i
\(989\) 93.0432 2.95860
\(990\) −7.98359 45.6107i −0.253735 1.44960i
\(991\) 30.8370 0.979570 0.489785 0.871843i \(-0.337075\pi\)
0.489785 + 0.871843i \(0.337075\pi\)
\(992\) 2.29361 + 2.29361i 0.0728221 + 0.0728221i
\(993\) −39.1900 39.1900i −1.24366 1.24366i
\(994\) 6.66397i 0.211368i
\(995\) 12.0014 14.3448i 0.380471 0.454759i
\(996\) 8.15440i 0.258382i
\(997\) −30.0148 30.0148i −0.950577 0.950577i 0.0482580 0.998835i \(-0.484633\pi\)
−0.998835 + 0.0482580i \(0.984633\pi\)
\(998\) −20.1833 + 20.1833i −0.638891 + 0.638891i
\(999\) 75.7305i 2.39601i
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 770.2.m.e.43.1 16
5.2 odd 4 inner 770.2.m.e.197.5 yes 16
11.10 odd 2 inner 770.2.m.e.43.5 yes 16
55.32 even 4 inner 770.2.m.e.197.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.m.e.43.1 16 1.1 even 1 trivial
770.2.m.e.43.5 yes 16 11.10 odd 2 inner
770.2.m.e.197.1 yes 16 55.32 even 4 inner
770.2.m.e.197.5 yes 16 5.2 odd 4 inner