Properties

Label 165.2.m.d.16.1
Level $165$
Weight $2$
Character 165.16
Analytic conductor $1.318$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(16,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.m (of order \(5\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.1
Root \(-0.386111 + 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 165.16
Dual form 165.2.m.d.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.456498 - 1.40496i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.147481 + 0.107152i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.456498 + 1.40496i) q^{6} +(1.85666 - 1.34895i) q^{7} +(-2.17239 - 1.57833i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.456498 - 1.40496i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.147481 + 0.107152i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.456498 + 1.40496i) q^{6} +(1.85666 - 1.34895i) q^{7} +(-2.17239 - 1.57833i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.47726 q^{10} +(-3.12020 + 1.12443i) q^{11} +0.182297 q^{12} +(-0.661536 - 2.03600i) q^{13} +(-2.74278 - 1.99274i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-1.33846 + 4.11937i) q^{16} +(0.168243 - 0.517799i) q^{17} +(1.19513 - 0.868312i) q^{18} +(1.76552 + 1.28272i) q^{19} +(0.0563329 + 0.173375i) q^{20} -2.29496 q^{21} +(3.00415 + 3.87045i) q^{22} +2.03908 q^{23} +(0.829779 + 2.55380i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.55850 + 1.85886i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.129282 + 0.397889i) q^{28} +(8.04603 - 5.84578i) q^{29} +(1.19513 + 0.868312i) q^{30} +(2.09249 + 6.44002i) q^{31} +1.02811 q^{32} +(3.18522 + 0.924324i) q^{33} -0.804288 q^{34} +(-0.709183 - 2.18264i) q^{35} +(-0.147481 - 0.107152i) q^{36} +(7.13520 - 5.18403i) q^{37} +(0.996215 - 3.06604i) q^{38} +(-0.661536 + 2.03600i) q^{39} +(-2.17239 + 1.57833i) q^{40} +(1.47470 + 1.07143i) q^{41} +(1.04765 + 3.22433i) q^{42} -0.620713 q^{43} +(0.339687 - 0.500167i) q^{44} +1.00000 q^{45} +(-0.930836 - 2.86482i) q^{46} +(0.305816 + 0.222188i) q^{47} +(3.50415 - 2.54591i) q^{48} +(-0.535571 + 1.64832i) q^{49} +(-0.456498 + 1.40496i) q^{50} +(-0.440466 + 0.320017i) q^{51} +(0.315724 + 0.229387i) q^{52} +(3.58246 + 11.0257i) q^{53} -1.47726 q^{54} +(0.105203 + 3.31496i) q^{55} -6.16248 q^{56} +(-0.674367 - 2.07549i) q^{57} +(-11.8861 - 8.63574i) q^{58} +(6.53518 - 4.74808i) q^{59} +(0.0563329 - 0.173375i) q^{60} +(2.69647 - 8.29887i) q^{61} +(8.09273 - 5.87971i) q^{62} +(1.85666 + 1.34895i) q^{63} +(2.20760 + 6.79429i) q^{64} -2.14077 q^{65} +(-0.155412 - 4.89705i) q^{66} -9.75802 q^{67} +(0.0306702 + 0.0943932i) q^{68} +(-1.64965 - 1.19854i) q^{69} +(-2.74278 + 1.99274i) q^{70} +(-4.63426 + 14.2628i) q^{71} +(0.829779 - 2.55380i) q^{72} +(-6.35761 + 4.61907i) q^{73} +(-10.5405 - 7.65815i) q^{74} +(0.309017 + 0.951057i) q^{75} -0.397826 q^{76} +(-4.27637 + 6.29667i) q^{77} +3.16248 q^{78} +(-2.85054 - 8.77306i) q^{79} +(3.50415 + 2.54591i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.832118 - 2.56099i) q^{82} +(-2.92093 + 8.98969i) q^{83} +(0.338464 - 0.245909i) q^{84} +(-0.440466 - 0.320017i) q^{85} +(0.283354 + 0.872075i) q^{86} -9.94544 q^{87} +(8.55302 + 2.48201i) q^{88} +0.583290 q^{89} +(-0.456498 - 1.40496i) q^{90} +(-3.97470 - 2.88779i) q^{91} +(-0.300726 + 0.218490i) q^{92} +(2.09249 - 6.44002i) q^{93} +(0.172561 - 0.531087i) q^{94} +(1.76552 - 1.28272i) q^{95} +(-0.831757 - 0.604307i) q^{96} +(-1.66190 - 5.11479i) q^{97} +2.56031 q^{98} +(-2.03359 - 2.62002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - q^{8} - 2 q^{9} - 6 q^{10} + 3 q^{11} + 2 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 12 q^{16} - q^{18} + 2 q^{19} - 3 q^{20} - 12 q^{21} + 9 q^{22} - 6 q^{23} + 4 q^{24} - 2 q^{25} + 2 q^{26} - 2 q^{27} - 11 q^{28} + 10 q^{29} - q^{30} + 19 q^{31} + 12 q^{32} - 2 q^{33} - 6 q^{34} + 3 q^{35} + 2 q^{36} - q^{37} - 20 q^{38} - 4 q^{39} - q^{40} - 9 q^{41} + q^{42} + 17 q^{44} + 8 q^{45} - 22 q^{46} - 19 q^{47} + 13 q^{48} + q^{49} + 4 q^{50} + 10 q^{51} - 2 q^{52} + 25 q^{53} - 6 q^{54} + 3 q^{55} - 16 q^{56} + 7 q^{57} - 12 q^{58} + 13 q^{59} - 3 q^{60} + 13 q^{61} + 35 q^{62} + 3 q^{63} + 39 q^{64} - 14 q^{65} - 11 q^{66} + 2 q^{67} + 19 q^{68} + 9 q^{69} - 4 q^{70} - 11 q^{71} + 4 q^{72} - 7 q^{73} - 43 q^{74} - 2 q^{75} - 38 q^{76} - 7 q^{77} - 8 q^{78} - 22 q^{79} + 13 q^{80} - 2 q^{81} - 35 q^{82} - 21 q^{83} + 4 q^{84} + 10 q^{85} + 20 q^{86} - 30 q^{87} + 59 q^{88} - 20 q^{89} + 4 q^{90} - 11 q^{91} - 28 q^{92} + 19 q^{93} - 35 q^{94} + 2 q^{95} - 8 q^{96} + 31 q^{97} + 22 q^{98} - 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.456498 1.40496i −0.322793 0.993455i −0.972427 0.233208i \(-0.925078\pi\)
0.649634 0.760247i \(-0.274922\pi\)
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) −0.147481 + 0.107152i −0.0737407 + 0.0535758i
\(5\) 0.309017 0.951057i 0.138197 0.425325i
\(6\) −0.456498 + 1.40496i −0.186365 + 0.573572i
\(7\) 1.85666 1.34895i 0.701753 0.509853i −0.178750 0.983895i \(-0.557205\pi\)
0.880503 + 0.474041i \(0.157205\pi\)
\(8\) −2.17239 1.57833i −0.768055 0.558025i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) −1.47726 −0.467151
\(11\) −3.12020 + 1.12443i −0.940776 + 0.339029i
\(12\) 0.182297 0.0526246
\(13\) −0.661536 2.03600i −0.183477 0.564684i 0.816442 0.577428i \(-0.195943\pi\)
−0.999919 + 0.0127437i \(0.995943\pi\)
\(14\) −2.74278 1.99274i −0.733038 0.532583i
\(15\) −0.809017 + 0.587785i −0.208887 + 0.151765i
\(16\) −1.33846 + 4.11937i −0.334616 + 1.02984i
\(17\) 0.168243 0.517799i 0.0408049 0.125585i −0.928579 0.371135i \(-0.878969\pi\)
0.969384 + 0.245550i \(0.0789687\pi\)
\(18\) 1.19513 0.868312i 0.281694 0.204663i
\(19\) 1.76552 + 1.28272i 0.405037 + 0.294277i 0.771590 0.636121i \(-0.219462\pi\)
−0.366553 + 0.930397i \(0.619462\pi\)
\(20\) 0.0563329 + 0.173375i 0.0125964 + 0.0387678i
\(21\) −2.29496 −0.500802
\(22\) 3.00415 + 3.87045i 0.640486 + 0.825183i
\(23\) 2.03908 0.425177 0.212589 0.977142i \(-0.431811\pi\)
0.212589 + 0.977142i \(0.431811\pi\)
\(24\) 0.829779 + 2.55380i 0.169378 + 0.521291i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) −2.55850 + 1.85886i −0.501763 + 0.364552i
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) −0.129282 + 0.397889i −0.0244320 + 0.0751939i
\(29\) 8.04603 5.84578i 1.49411 1.08553i 0.521455 0.853279i \(-0.325389\pi\)
0.972655 0.232256i \(-0.0746107\pi\)
\(30\) 1.19513 + 0.868312i 0.218200 + 0.158531i
\(31\) 2.09249 + 6.44002i 0.375822 + 1.15666i 0.942922 + 0.333012i \(0.108065\pi\)
−0.567101 + 0.823649i \(0.691935\pi\)
\(32\) 1.02811 0.181746
\(33\) 3.18522 + 0.924324i 0.554476 + 0.160904i
\(34\) −0.804288 −0.137934
\(35\) −0.709183 2.18264i −0.119874 0.368933i
\(36\) −0.147481 0.107152i −0.0245802 0.0178586i
\(37\) 7.13520 5.18403i 1.17302 0.852249i 0.181652 0.983363i \(-0.441855\pi\)
0.991367 + 0.131114i \(0.0418555\pi\)
\(38\) 0.996215 3.06604i 0.161607 0.497377i
\(39\) −0.661536 + 2.03600i −0.105930 + 0.326020i
\(40\) −2.17239 + 1.57833i −0.343485 + 0.249556i
\(41\) 1.47470 + 1.07143i 0.230309 + 0.167329i 0.696955 0.717115i \(-0.254538\pi\)
−0.466646 + 0.884444i \(0.654538\pi\)
\(42\) 1.04765 + 3.22433i 0.161655 + 0.497524i
\(43\) −0.620713 −0.0946578 −0.0473289 0.998879i \(-0.515071\pi\)
−0.0473289 + 0.998879i \(0.515071\pi\)
\(44\) 0.339687 0.500167i 0.0512098 0.0754030i
\(45\) 1.00000 0.149071
\(46\) −0.930836 2.86482i −0.137244 0.422394i
\(47\) 0.305816 + 0.222188i 0.0446078 + 0.0324095i 0.609866 0.792505i \(-0.291223\pi\)
−0.565258 + 0.824914i \(0.691223\pi\)
\(48\) 3.50415 2.54591i 0.505780 0.367471i
\(49\) −0.535571 + 1.64832i −0.0765102 + 0.235474i
\(50\) −0.456498 + 1.40496i −0.0645586 + 0.198691i
\(51\) −0.440466 + 0.320017i −0.0616776 + 0.0448114i
\(52\) 0.315724 + 0.229387i 0.0437831 + 0.0318103i
\(53\) 3.58246 + 11.0257i 0.492089 + 1.51449i 0.821445 + 0.570288i \(0.193169\pi\)
−0.329355 + 0.944206i \(0.606831\pi\)
\(54\) −1.47726 −0.201030
\(55\) 0.105203 + 3.31496i 0.0141855 + 0.446989i
\(56\) −6.16248 −0.823496
\(57\) −0.674367 2.07549i −0.0893221 0.274905i
\(58\) −11.8861 8.63574i −1.56072 1.13393i
\(59\) 6.53518 4.74808i 0.850807 0.618148i −0.0745611 0.997216i \(-0.523756\pi\)
0.925369 + 0.379069i \(0.123756\pi\)
\(60\) 0.0563329 0.173375i 0.00727255 0.0223826i
\(61\) 2.69647 8.29887i 0.345247 1.06256i −0.616204 0.787587i \(-0.711330\pi\)
0.961451 0.274975i \(-0.0886697\pi\)
\(62\) 8.09273 5.87971i 1.02778 0.746724i
\(63\) 1.85666 + 1.34895i 0.233918 + 0.169951i
\(64\) 2.20760 + 6.79429i 0.275950 + 0.849286i
\(65\) −2.14077 −0.265530
\(66\) −0.155412 4.89705i −0.0191299 0.602785i
\(67\) −9.75802 −1.19213 −0.596066 0.802936i \(-0.703270\pi\)
−0.596066 + 0.802936i \(0.703270\pi\)
\(68\) 0.0306702 + 0.0943932i 0.00371931 + 0.0114469i
\(69\) −1.64965 1.19854i −0.198594 0.144287i
\(70\) −2.74278 + 1.99274i −0.327824 + 0.238178i
\(71\) −4.63426 + 14.2628i −0.549985 + 1.69268i 0.158848 + 0.987303i \(0.449222\pi\)
−0.708833 + 0.705376i \(0.750778\pi\)
\(72\) 0.829779 2.55380i 0.0977903 0.300968i
\(73\) −6.35761 + 4.61907i −0.744102 + 0.540622i −0.893993 0.448081i \(-0.852108\pi\)
0.149891 + 0.988702i \(0.452108\pi\)
\(74\) −10.5405 7.65815i −1.22531 0.890242i
\(75\) 0.309017 + 0.951057i 0.0356822 + 0.109819i
\(76\) −0.397826 −0.0456338
\(77\) −4.27637 + 6.29667i −0.487337 + 0.717572i
\(78\) 3.16248 0.358080
\(79\) −2.85054 8.77306i −0.320711 0.987046i −0.973340 0.229369i \(-0.926334\pi\)
0.652629 0.757678i \(-0.273666\pi\)
\(80\) 3.50415 + 2.54591i 0.391775 + 0.284641i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0.832118 2.56099i 0.0918920 0.282815i
\(83\) −2.92093 + 8.98969i −0.320613 + 0.986747i 0.652769 + 0.757557i \(0.273607\pi\)
−0.973382 + 0.229189i \(0.926393\pi\)
\(84\) 0.338464 0.245909i 0.0369295 0.0268309i
\(85\) −0.440466 0.320017i −0.0477752 0.0347107i
\(86\) 0.283354 + 0.872075i 0.0305549 + 0.0940383i
\(87\) −9.94544 −1.06626
\(88\) 8.55302 + 2.48201i 0.911754 + 0.264583i
\(89\) 0.583290 0.0618287 0.0309143 0.999522i \(-0.490158\pi\)
0.0309143 + 0.999522i \(0.490158\pi\)
\(90\) −0.456498 1.40496i −0.0481192 0.148096i
\(91\) −3.97470 2.88779i −0.416662 0.302722i
\(92\) −0.300726 + 0.218490i −0.0313529 + 0.0227792i
\(93\) 2.09249 6.44002i 0.216981 0.667798i
\(94\) 0.172561 0.531087i 0.0177983 0.0547774i
\(95\) 1.76552 1.28272i 0.181138 0.131605i
\(96\) −0.831757 0.604307i −0.0848908 0.0616768i
\(97\) −1.66190 5.11479i −0.168740 0.519328i 0.830552 0.556940i \(-0.188025\pi\)
−0.999292 + 0.0376122i \(0.988025\pi\)
\(98\) 2.56031 0.258630
\(99\) −2.03359 2.62002i −0.204384 0.263322i
\(100\) 0.182297 0.0182297
\(101\) −6.03482 18.5733i −0.600487 1.84811i −0.525261 0.850941i \(-0.676032\pi\)
−0.0752256 0.997167i \(-0.523968\pi\)
\(102\) 0.650683 + 0.472749i 0.0644272 + 0.0468091i
\(103\) −10.5223 + 7.64487i −1.03679 + 0.753271i −0.969656 0.244473i \(-0.921385\pi\)
−0.0671325 + 0.997744i \(0.521385\pi\)
\(104\) −1.77637 + 5.46710i −0.174187 + 0.536093i
\(105\) −0.709183 + 2.18264i −0.0692091 + 0.213004i
\(106\) 13.8552 10.0664i 1.34574 0.977737i
\(107\) −1.59663 1.16002i −0.154352 0.112144i 0.507928 0.861399i \(-0.330411\pi\)
−0.662281 + 0.749256i \(0.730411\pi\)
\(108\) 0.0563329 + 0.173375i 0.00542064 + 0.0166830i
\(109\) 10.6212 1.01733 0.508663 0.860966i \(-0.330140\pi\)
0.508663 + 0.860966i \(0.330140\pi\)
\(110\) 4.60935 1.66108i 0.439484 0.158378i
\(111\) −8.81959 −0.837119
\(112\) 3.07173 + 9.45380i 0.290251 + 0.893300i
\(113\) 13.6688 + 9.93096i 1.28585 + 0.934226i 0.999713 0.0239621i \(-0.00762811\pi\)
0.286139 + 0.958188i \(0.407628\pi\)
\(114\) −2.60813 + 1.89491i −0.244273 + 0.177475i
\(115\) 0.630110 1.93928i 0.0587580 0.180839i
\(116\) −0.560255 + 1.72429i −0.0520184 + 0.160096i
\(117\) 1.73192 1.25832i 0.160116 0.116331i
\(118\) −9.65415 7.01415i −0.888737 0.645705i
\(119\) −0.386111 1.18833i −0.0353948 0.108934i
\(120\) 2.68522 0.245126
\(121\) 8.47131 7.01690i 0.770119 0.637900i
\(122\) −12.8905 −1.16705
\(123\) −0.563285 1.73361i −0.0507897 0.156314i
\(124\) −0.998661 0.725569i −0.0896824 0.0651581i
\(125\) −0.809017 + 0.587785i −0.0723607 + 0.0525731i
\(126\) 1.04765 3.22433i 0.0933318 0.287246i
\(127\) 1.27701 3.93022i 0.113316 0.348751i −0.878276 0.478154i \(-0.841306\pi\)
0.991592 + 0.129403i \(0.0413061\pi\)
\(128\) 10.2014 7.41178i 0.901689 0.655115i
\(129\) 0.502167 + 0.364846i 0.0442133 + 0.0321229i
\(130\) 0.977260 + 3.00770i 0.0857114 + 0.263792i
\(131\) −0.436527 −0.0381395 −0.0190698 0.999818i \(-0.506070\pi\)
−0.0190698 + 0.999818i \(0.506070\pi\)
\(132\) −0.568804 + 0.204981i −0.0495080 + 0.0178413i
\(133\) 5.00829 0.434274
\(134\) 4.45452 + 13.7096i 0.384812 + 1.18433i
\(135\) −0.809017 0.587785i −0.0696291 0.0505885i
\(136\) −1.18275 + 0.859317i −0.101420 + 0.0736858i
\(137\) −2.43131 + 7.48281i −0.207721 + 0.639300i 0.791870 + 0.610690i \(0.209108\pi\)
−0.999591 + 0.0286095i \(0.990892\pi\)
\(138\) −0.930836 + 2.86482i −0.0792380 + 0.243869i
\(139\) −14.2736 + 10.3704i −1.21067 + 0.879604i −0.995292 0.0969265i \(-0.969099\pi\)
−0.215379 + 0.976530i \(0.569099\pi\)
\(140\) 0.338464 + 0.245909i 0.0286055 + 0.0207831i
\(141\) −0.116811 0.359508i −0.00983728 0.0302760i
\(142\) 22.1541 1.85913
\(143\) 4.35346 + 5.60887i 0.364055 + 0.469037i
\(144\) −4.33136 −0.360947
\(145\) −3.07331 9.45867i −0.255224 0.785500i
\(146\) 9.39184 + 6.82357i 0.777274 + 0.564723i
\(147\) 1.40214 1.01872i 0.115647 0.0840224i
\(148\) −0.496833 + 1.52910i −0.0408394 + 0.125691i
\(149\) −3.38687 + 10.4237i −0.277463 + 0.853943i 0.711094 + 0.703097i \(0.248200\pi\)
−0.988557 + 0.150846i \(0.951800\pi\)
\(150\) 1.19513 0.868312i 0.0975818 0.0708973i
\(151\) 16.2065 + 11.7747i 1.31887 + 0.958214i 0.999946 + 0.0104337i \(0.00332120\pi\)
0.318923 + 0.947781i \(0.396679\pi\)
\(152\) −1.81082 5.57314i −0.146877 0.452041i
\(153\) 0.544446 0.0440158
\(154\) 10.7987 + 3.13370i 0.870185 + 0.252520i
\(155\) 6.77143 0.543895
\(156\) −0.120596 0.371156i −0.00965541 0.0297163i
\(157\) −7.40629 5.38098i −0.591086 0.429449i 0.251618 0.967827i \(-0.419037\pi\)
−0.842704 + 0.538377i \(0.819037\pi\)
\(158\) −11.0245 + 8.00978i −0.877063 + 0.637224i
\(159\) 3.58246 11.0257i 0.284108 0.874394i
\(160\) 0.317703 0.977789i 0.0251166 0.0773010i
\(161\) 3.78588 2.75060i 0.298369 0.216778i
\(162\) 1.19513 + 0.868312i 0.0938982 + 0.0682210i
\(163\) −3.50181 10.7775i −0.274283 0.844155i −0.989408 0.145159i \(-0.953631\pi\)
0.715126 0.698996i \(-0.246369\pi\)
\(164\) −0.332296 −0.0259480
\(165\) 1.86337 2.74369i 0.145063 0.213596i
\(166\) 13.9635 1.08378
\(167\) 4.66619 + 14.3611i 0.361081 + 1.11129i 0.952399 + 0.304854i \(0.0986077\pi\)
−0.591318 + 0.806438i \(0.701392\pi\)
\(168\) 4.98555 + 3.62221i 0.384644 + 0.279460i
\(169\) 6.80957 4.94744i 0.523813 0.380572i
\(170\) −0.248539 + 0.764923i −0.0190620 + 0.0586669i
\(171\) −0.674367 + 2.07549i −0.0515701 + 0.158717i
\(172\) 0.0915436 0.0665103i 0.00698013 0.00507136i
\(173\) −14.7760 10.7354i −1.12340 0.816195i −0.138676 0.990338i \(-0.544285\pi\)
−0.984720 + 0.174143i \(0.944285\pi\)
\(174\) 4.54008 + 13.9729i 0.344182 + 1.05928i
\(175\) −2.29496 −0.173483
\(176\) −0.455671 14.3583i −0.0343475 1.08230i
\(177\) −8.07792 −0.607174
\(178\) −0.266271 0.819498i −0.0199579 0.0614240i
\(179\) 0.425073 + 0.308833i 0.0317714 + 0.0230833i 0.603558 0.797319i \(-0.293749\pi\)
−0.571786 + 0.820403i \(0.693749\pi\)
\(180\) −0.147481 + 0.107152i −0.0109926 + 0.00798660i
\(181\) −5.47289 + 16.8438i −0.406797 + 1.25199i 0.512589 + 0.858634i \(0.328687\pi\)
−0.919386 + 0.393358i \(0.871313\pi\)
\(182\) −2.24278 + 6.90255i −0.166246 + 0.511651i
\(183\) −7.05944 + 5.12899i −0.521849 + 0.379146i
\(184\) −4.42967 3.21834i −0.326560 0.237259i
\(185\) −2.72540 8.38793i −0.200376 0.616693i
\(186\) −10.0032 −0.733468
\(187\) 0.0572771 + 1.80481i 0.00418852 + 0.131981i
\(188\) −0.0689100 −0.00502578
\(189\) −0.709183 2.18264i −0.0515854 0.158764i
\(190\) −2.60813 1.89491i −0.189213 0.137472i
\(191\) 13.3908 9.72899i 0.968925 0.703965i 0.0137185 0.999906i \(-0.495633\pi\)
0.955206 + 0.295941i \(0.0956331\pi\)
\(192\) 2.20760 6.79429i 0.159320 0.490336i
\(193\) −7.57191 + 23.3040i −0.545038 + 1.67746i 0.175860 + 0.984415i \(0.443729\pi\)
−0.720899 + 0.693040i \(0.756271\pi\)
\(194\) −6.42741 + 4.66979i −0.461461 + 0.335271i
\(195\) 1.73192 + 1.25832i 0.124026 + 0.0901098i
\(196\) −0.0976331 0.300484i −0.00697379 0.0214631i
\(197\) −7.50877 −0.534978 −0.267489 0.963561i \(-0.586194\pi\)
−0.267489 + 0.963561i \(0.586194\pi\)
\(198\) −2.75268 + 4.05315i −0.195625 + 0.288045i
\(199\) −20.0956 −1.42454 −0.712270 0.701906i \(-0.752333\pi\)
−0.712270 + 0.701906i \(0.752333\pi\)
\(200\) 0.829779 + 2.55380i 0.0586742 + 0.180581i
\(201\) 7.89440 + 5.73562i 0.556828 + 0.404559i
\(202\) −23.3398 + 16.9573i −1.64218 + 1.19311i
\(203\) 7.05313 21.7073i 0.495033 1.52355i
\(204\) 0.0306702 0.0943932i 0.00214734 0.00660885i
\(205\) 1.47470 1.07143i 0.102997 0.0748320i
\(206\) 15.5441 + 11.2935i 1.08301 + 0.786852i
\(207\) 0.630110 + 1.93928i 0.0437956 + 0.134789i
\(208\) 9.27247 0.642930
\(209\) −6.95110 2.01715i −0.480817 0.139529i
\(210\) 3.39026 0.233950
\(211\) 1.67444 + 5.15339i 0.115273 + 0.354774i 0.992004 0.126207i \(-0.0402804\pi\)
−0.876731 + 0.480981i \(0.840280\pi\)
\(212\) −1.70977 1.24222i −0.117427 0.0853159i
\(213\) 12.1326 8.81488i 0.831315 0.603985i
\(214\) −0.900921 + 2.77275i −0.0615857 + 0.189541i
\(215\) −0.191811 + 0.590333i −0.0130814 + 0.0402604i
\(216\) −2.17239 + 1.57833i −0.147812 + 0.107392i
\(217\) 12.5723 + 9.13429i 0.853462 + 0.620076i
\(218\) −4.84856 14.9223i −0.328386 1.01067i
\(219\) 7.85844 0.531024
\(220\) −0.370718 0.477622i −0.0249938 0.0322013i
\(221\) −1.16554 −0.0784024
\(222\) 4.02613 + 12.3912i 0.270216 + 0.831640i
\(223\) −12.7076 9.23259i −0.850961 0.618260i 0.0744495 0.997225i \(-0.476280\pi\)
−0.925411 + 0.378965i \(0.876280\pi\)
\(224\) 1.90885 1.38686i 0.127541 0.0926636i
\(225\) 0.309017 0.951057i 0.0206011 0.0634038i
\(226\) 7.71280 23.7375i 0.513048 1.57900i
\(227\) 1.19040 0.864876i 0.0790096 0.0574038i −0.547579 0.836754i \(-0.684451\pi\)
0.626589 + 0.779350i \(0.284451\pi\)
\(228\) 0.321848 + 0.233837i 0.0213149 + 0.0154862i
\(229\) −4.93656 15.1932i −0.326217 1.00399i −0.970888 0.239533i \(-0.923006\pi\)
0.644671 0.764460i \(-0.276994\pi\)
\(230\) −3.01225 −0.198622
\(231\) 7.16075 2.58053i 0.471142 0.169786i
\(232\) −26.7057 −1.75331
\(233\) −7.92263 24.3833i −0.519029 1.59741i −0.775830 0.630942i \(-0.782669\pi\)
0.256802 0.966464i \(-0.417331\pi\)
\(234\) −2.55850 1.85886i −0.167254 0.121517i
\(235\) 0.305816 0.222188i 0.0199492 0.0144940i
\(236\) −0.455053 + 1.40051i −0.0296214 + 0.0911653i
\(237\) −2.85054 + 8.77306i −0.185162 + 0.569872i
\(238\) −1.49329 + 1.08494i −0.0967958 + 0.0703262i
\(239\) 3.38336 + 2.45816i 0.218851 + 0.159005i 0.691809 0.722080i \(-0.256814\pi\)
−0.472958 + 0.881085i \(0.656814\pi\)
\(240\) −1.33846 4.11937i −0.0863975 0.265904i
\(241\) −3.29180 −0.212043 −0.106022 0.994364i \(-0.533811\pi\)
−0.106022 + 0.994364i \(0.533811\pi\)
\(242\) −13.7256 8.69862i −0.882314 0.559169i
\(243\) 1.00000 0.0641500
\(244\) 0.491558 + 1.51286i 0.0314688 + 0.0968510i
\(245\) 1.40214 + 1.01872i 0.0895797 + 0.0650835i
\(246\) −2.17851 + 1.58278i −0.138897 + 0.100914i
\(247\) 1.44367 4.44315i 0.0918583 0.282711i
\(248\) 5.61879 17.2929i 0.356794 1.09810i
\(249\) 7.64709 5.55593i 0.484614 0.352093i
\(250\) 1.19513 + 0.868312i 0.0755866 + 0.0549169i
\(251\) −2.89382 8.90626i −0.182656 0.562158i 0.817244 0.576292i \(-0.195501\pi\)
−0.999900 + 0.0141339i \(0.995501\pi\)
\(252\) −0.418365 −0.0263545
\(253\) −6.36233 + 2.29280i −0.399996 + 0.144147i
\(254\) −6.10475 −0.383046
\(255\) 0.168243 + 0.517799i 0.0105358 + 0.0324258i
\(256\) −3.51104 2.55092i −0.219440 0.159433i
\(257\) 10.1705 7.38928i 0.634416 0.460930i −0.223511 0.974701i \(-0.571752\pi\)
0.857927 + 0.513771i \(0.171752\pi\)
\(258\) 0.283354 0.872075i 0.0176409 0.0542930i
\(259\) 6.25470 19.2500i 0.388648 1.19614i
\(260\) 0.315724 0.229387i 0.0195804 0.0142260i
\(261\) 8.04603 + 5.84578i 0.498037 + 0.361845i
\(262\) 0.199274 + 0.613302i 0.0123112 + 0.0378899i
\(263\) 4.82946 0.297797 0.148899 0.988852i \(-0.452427\pi\)
0.148899 + 0.988852i \(0.452427\pi\)
\(264\) −5.46064 7.03533i −0.336079 0.432994i
\(265\) 11.5931 0.712158
\(266\) −2.28628 7.03644i −0.140181 0.431432i
\(267\) −0.471892 0.342849i −0.0288793 0.0209820i
\(268\) 1.43913 1.04559i 0.0879087 0.0638694i
\(269\) −1.61594 + 4.97335i −0.0985255 + 0.303230i −0.988156 0.153450i \(-0.950962\pi\)
0.889631 + 0.456680i \(0.150962\pi\)
\(270\) −0.456498 + 1.40496i −0.0277816 + 0.0855030i
\(271\) −24.5383 + 17.8281i −1.49060 + 1.08298i −0.516654 + 0.856194i \(0.672823\pi\)
−0.973944 + 0.226789i \(0.927177\pi\)
\(272\) 1.90782 + 1.38611i 0.115678 + 0.0840453i
\(273\) 1.51820 + 4.67254i 0.0918856 + 0.282795i
\(274\) 11.6229 0.702167
\(275\) 3.18522 + 0.924324i 0.192076 + 0.0557388i
\(276\) 0.371718 0.0223748
\(277\) 4.93483 + 15.1878i 0.296505 + 0.912549i 0.982712 + 0.185142i \(0.0592746\pi\)
−0.686206 + 0.727407i \(0.740725\pi\)
\(278\) 21.0858 + 15.3197i 1.26464 + 0.918817i
\(279\) −5.47820 + 3.98015i −0.327972 + 0.238285i
\(280\) −1.90431 + 5.86087i −0.113804 + 0.350254i
\(281\) −0.429741 + 1.32261i −0.0256362 + 0.0789000i −0.963056 0.269301i \(-0.913207\pi\)
0.937420 + 0.348201i \(0.113207\pi\)
\(282\) −0.451769 + 0.328230i −0.0269025 + 0.0195458i
\(283\) −4.75259 3.45296i −0.282512 0.205257i 0.437500 0.899218i \(-0.355864\pi\)
−0.720013 + 0.693961i \(0.755864\pi\)
\(284\) −0.844811 2.60006i −0.0501303 0.154285i
\(285\) −2.18230 −0.129268
\(286\) 5.89287 8.67687i 0.348453 0.513074i
\(287\) 4.18332 0.246934
\(288\) 0.317703 + 0.977789i 0.0187208 + 0.0576168i
\(289\) 13.5135 + 9.81812i 0.794911 + 0.577536i
\(290\) −11.8861 + 8.63574i −0.697974 + 0.507108i
\(291\) −1.66190 + 5.11479i −0.0974221 + 0.299834i
\(292\) 0.442688 1.36246i 0.0259064 0.0797317i
\(293\) −16.1597 + 11.7407i −0.944060 + 0.685900i −0.949395 0.314086i \(-0.898302\pi\)
0.00533421 + 0.999986i \(0.498302\pi\)
\(294\) −2.07133 1.50491i −0.120802 0.0877681i
\(295\) −2.49622 7.68256i −0.145335 0.447296i
\(296\) −23.6825 −1.37652
\(297\) 0.105203 + 3.31496i 0.00610448 + 0.192353i
\(298\) 16.1910 0.937917
\(299\) −1.34892 4.15156i −0.0780102 0.240091i
\(300\) −0.147481 0.107152i −0.00851485 0.00618640i
\(301\) −1.15245 + 0.837307i −0.0664264 + 0.0482616i
\(302\) 9.14475 28.1446i 0.526221 1.61954i
\(303\) −6.03482 + 18.5733i −0.346691 + 1.06701i
\(304\) −7.64709 + 5.55593i −0.438590 + 0.318655i
\(305\) −7.05944 5.12899i −0.404223 0.293685i
\(306\) −0.248539 0.764923i −0.0142080 0.0437278i
\(307\) 19.4372 1.10934 0.554671 0.832070i \(-0.312844\pi\)
0.554671 + 0.832070i \(0.312844\pi\)
\(308\) −0.0440131 1.38686i −0.00250788 0.0790238i
\(309\) 13.0062 0.739898
\(310\) −3.09115 9.51358i −0.175565 0.540335i
\(311\) −4.87175 3.53954i −0.276252 0.200709i 0.441029 0.897493i \(-0.354614\pi\)
−0.717281 + 0.696784i \(0.754614\pi\)
\(312\) 4.65059 3.37885i 0.263288 0.191290i
\(313\) −1.57856 + 4.85831i −0.0892256 + 0.274608i −0.985706 0.168476i \(-0.946116\pi\)
0.896480 + 0.443084i \(0.146116\pi\)
\(314\) −4.17910 + 12.8619i −0.235840 + 0.725841i
\(315\) 1.85666 1.34895i 0.104611 0.0760045i
\(316\) 1.36045 + 0.988424i 0.0765312 + 0.0556032i
\(317\) 4.22699 + 13.0093i 0.237411 + 0.730677i 0.996792 + 0.0800306i \(0.0255018\pi\)
−0.759381 + 0.650646i \(0.774498\pi\)
\(318\) −17.1260 −0.960379
\(319\) −18.5320 + 27.2872i −1.03760 + 1.52779i
\(320\) 7.14394 0.399358
\(321\) 0.609860 + 1.87695i 0.0340390 + 0.104761i
\(322\) −5.59273 4.06336i −0.311671 0.226442i
\(323\) 0.961227 0.698373i 0.0534841 0.0388585i
\(324\) 0.0563329 0.173375i 0.00312961 0.00963194i
\(325\) −0.661536 + 2.03600i −0.0366954 + 0.112937i
\(326\) −13.5433 + 9.83978i −0.750094 + 0.544975i
\(327\) −8.59273 6.24299i −0.475179 0.345238i
\(328\) −1.51254 4.65513i −0.0835162 0.257036i
\(329\) 0.867517 0.0478278
\(330\) −4.70540 1.36547i −0.259024 0.0751665i
\(331\) 11.4695 0.630418 0.315209 0.949022i \(-0.397925\pi\)
0.315209 + 0.949022i \(0.397925\pi\)
\(332\) −0.532477 1.63879i −0.0292234 0.0899405i
\(333\) 7.13520 + 5.18403i 0.391007 + 0.284083i
\(334\) 18.0466 13.1116i 0.987465 0.717435i
\(335\) −3.01539 + 9.28043i −0.164749 + 0.507044i
\(336\) 3.07173 9.45380i 0.167576 0.515747i
\(337\) −3.04517 + 2.21245i −0.165881 + 0.120520i −0.667629 0.744494i \(-0.732691\pi\)
0.501748 + 0.865014i \(0.332691\pi\)
\(338\) −10.0595 7.30865i −0.547165 0.397538i
\(339\) −5.22101 16.0686i −0.283567 0.872728i
\(340\) 0.0992509 0.00538264
\(341\) −13.7703 17.7413i −0.745706 0.960744i
\(342\) 3.22382 0.174324
\(343\) 6.19339 + 19.0613i 0.334412 + 1.02921i
\(344\) 1.34843 + 0.979691i 0.0727024 + 0.0528214i
\(345\) −1.64965 + 1.19854i −0.0888141 + 0.0645272i
\(346\) −8.33754 + 25.6603i −0.448229 + 1.37951i
\(347\) −0.122365 + 0.376600i −0.00656888 + 0.0202169i −0.954287 0.298891i \(-0.903383\pi\)
0.947718 + 0.319108i \(0.103383\pi\)
\(348\) 1.46677 1.06567i 0.0786270 0.0571259i
\(349\) 10.6554 + 7.74158i 0.570369 + 0.414398i 0.835239 0.549887i \(-0.185329\pi\)
−0.264870 + 0.964284i \(0.585329\pi\)
\(350\) 1.04765 + 3.22433i 0.0559991 + 0.172347i
\(351\) −2.14077 −0.114266
\(352\) −3.20790 + 1.15604i −0.170982 + 0.0616170i
\(353\) 11.3853 0.605977 0.302989 0.952994i \(-0.402016\pi\)
0.302989 + 0.952994i \(0.402016\pi\)
\(354\) 3.68756 + 11.3491i 0.195992 + 0.603200i
\(355\) 12.1326 + 8.81488i 0.643934 + 0.467845i
\(356\) −0.0860245 + 0.0625005i −0.00455929 + 0.00331252i
\(357\) −0.386111 + 1.18833i −0.0204352 + 0.0628930i
\(358\) 0.239853 0.738191i 0.0126766 0.0390146i
\(359\) 11.6241 8.44543i 0.613499 0.445733i −0.237146 0.971474i \(-0.576212\pi\)
0.850645 + 0.525741i \(0.176212\pi\)
\(360\) −2.17239 1.57833i −0.114495 0.0831854i
\(361\) −4.39965 13.5407i −0.231561 0.712671i
\(362\) 26.1632 1.37511
\(363\) −10.9779 + 0.697484i −0.576188 + 0.0366084i
\(364\) 0.895625 0.0469435
\(365\) 2.42839 + 7.47382i 0.127108 + 0.391197i
\(366\) 10.4286 + 7.57685i 0.545113 + 0.396048i
\(367\) 21.2480 15.4376i 1.10914 0.805836i 0.126610 0.991953i \(-0.459590\pi\)
0.982528 + 0.186117i \(0.0595903\pi\)
\(368\) −2.72923 + 8.39972i −0.142271 + 0.437865i
\(369\) −0.563285 + 1.73361i −0.0293234 + 0.0902482i
\(370\) −10.5405 + 7.65815i −0.547977 + 0.398128i
\(371\) 21.5245 + 15.6384i 1.11750 + 0.811908i
\(372\) 0.381454 + 1.17400i 0.0197775 + 0.0608689i
\(373\) 21.8951 1.13368 0.566842 0.823827i \(-0.308165\pi\)
0.566842 + 0.823827i \(0.308165\pi\)
\(374\) 2.50954 0.904367i 0.129765 0.0467637i
\(375\) 1.00000 0.0516398
\(376\) −0.313664 0.965358i −0.0161760 0.0497845i
\(377\) −17.2247 12.5145i −0.887119 0.644529i
\(378\) −2.74278 + 1.99274i −0.141073 + 0.102496i
\(379\) 7.89836 24.3087i 0.405711 1.24865i −0.514588 0.857437i \(-0.672055\pi\)
0.920300 0.391214i \(-0.127945\pi\)
\(380\) −0.122935 + 0.378355i −0.00630644 + 0.0194092i
\(381\) −3.34325 + 2.42901i −0.171280 + 0.124442i
\(382\) −19.7817 14.3722i −1.01212 0.735348i
\(383\) 5.88737 + 18.1195i 0.300831 + 0.925862i 0.981200 + 0.192992i \(0.0618193\pi\)
−0.680370 + 0.732869i \(0.738181\pi\)
\(384\) −12.6097 −0.643485
\(385\) 4.66702 + 6.01285i 0.237853 + 0.306443i
\(386\) 36.1976 1.84241
\(387\) −0.191811 0.590333i −0.00975029 0.0300083i
\(388\) 0.793157 + 0.576262i 0.0402664 + 0.0292553i
\(389\) −13.2618 + 9.63528i −0.672401 + 0.488528i −0.870828 0.491587i \(-0.836417\pi\)
0.198427 + 0.980116i \(0.436417\pi\)
\(390\) 0.977260 3.00770i 0.0494855 0.152301i
\(391\) 0.343061 1.05583i 0.0173493 0.0533957i
\(392\) 3.76506 2.73548i 0.190164 0.138163i
\(393\) 0.353158 + 0.256584i 0.0178145 + 0.0129430i
\(394\) 3.42774 + 10.5495i 0.172687 + 0.531476i
\(395\) −9.22454 −0.464137
\(396\) 0.580656 + 0.168502i 0.0291791 + 0.00846752i
\(397\) 30.9826 1.55497 0.777485 0.628901i \(-0.216495\pi\)
0.777485 + 0.628901i \(0.216495\pi\)
\(398\) 9.17361 + 28.2335i 0.459832 + 1.41522i
\(399\) −4.05179 2.94380i −0.202843 0.147374i
\(400\) 3.50415 2.54591i 0.175207 0.127296i
\(401\) −1.96723 + 6.05453i −0.0982390 + 0.302349i −0.988084 0.153914i \(-0.950812\pi\)
0.889845 + 0.456262i \(0.150812\pi\)
\(402\) 4.45452 13.7096i 0.222171 0.683773i
\(403\) 11.7276 8.52060i 0.584193 0.424441i
\(404\) 2.88018 + 2.09257i 0.143294 + 0.104109i
\(405\) 0.309017 + 0.951057i 0.0153552 + 0.0472584i
\(406\) −33.7176 −1.67338
\(407\) −16.4342 + 24.1982i −0.814612 + 1.19946i
\(408\) 1.46196 0.0723776
\(409\) −1.93715 5.96193i −0.0957858 0.294798i 0.891672 0.452682i \(-0.149533\pi\)
−0.987458 + 0.157884i \(0.949533\pi\)
\(410\) −2.17851 1.58278i −0.107589 0.0781680i
\(411\) 6.36526 4.62463i 0.313975 0.228116i
\(412\) 0.732678 2.25495i 0.0360965 0.111093i
\(413\) 5.72872 17.6312i 0.281892 0.867574i
\(414\) 2.43696 1.77055i 0.119770 0.0870180i
\(415\) 7.64709 + 5.55593i 0.375381 + 0.272730i
\(416\) −0.680130 2.09323i −0.0333461 0.102629i
\(417\) 17.6431 0.863988
\(418\) 0.339154 + 10.6868i 0.0165886 + 0.522710i
\(419\) 3.90332 0.190689 0.0953447 0.995444i \(-0.469605\pi\)
0.0953447 + 0.995444i \(0.469605\pi\)
\(420\) −0.129282 0.397889i −0.00630831 0.0194150i
\(421\) −14.0539 10.2107i −0.684944 0.497641i 0.190050 0.981774i \(-0.439135\pi\)
−0.874994 + 0.484134i \(0.839135\pi\)
\(422\) 6.47592 4.70503i 0.315243 0.229037i
\(423\) −0.116811 + 0.359508i −0.00567956 + 0.0174799i
\(424\) 9.61970 29.6064i 0.467174 1.43781i
\(425\) −0.440466 + 0.320017i −0.0213657 + 0.0155231i
\(426\) −17.9231 13.0219i −0.868375 0.630911i
\(427\) −6.18829 19.0456i −0.299473 0.921682i
\(428\) 0.359772 0.0173902
\(429\) −0.225215 7.09657i −0.0108735 0.342626i
\(430\) 0.916954 0.0442194
\(431\) −2.17440 6.69212i −0.104737 0.322348i 0.884931 0.465721i \(-0.154205\pi\)
−0.989669 + 0.143373i \(0.954205\pi\)
\(432\) 3.50415 + 2.54591i 0.168593 + 0.122490i
\(433\) −2.22665 + 1.61776i −0.107006 + 0.0777445i −0.640002 0.768374i \(-0.721066\pi\)
0.532995 + 0.846118i \(0.321066\pi\)
\(434\) 7.09407 21.8333i 0.340526 1.04803i
\(435\) −3.07331 + 9.45867i −0.147354 + 0.453509i
\(436\) −1.56643 + 1.13808i −0.0750184 + 0.0545041i
\(437\) 3.60002 + 2.61557i 0.172212 + 0.125120i
\(438\) −3.58736 11.0408i −0.171411 0.527548i
\(439\) −2.73703 −0.130631 −0.0653157 0.997865i \(-0.520805\pi\)
−0.0653157 + 0.997865i \(0.520805\pi\)
\(440\) 5.00356 7.36742i 0.238535 0.351228i
\(441\) −1.73315 −0.0825307
\(442\) 0.532065 + 1.63753i 0.0253078 + 0.0778893i
\(443\) −8.98348 6.52688i −0.426818 0.310102i 0.353557 0.935413i \(-0.384972\pi\)
−0.780375 + 0.625311i \(0.784972\pi\)
\(444\) 1.30073 0.945033i 0.0617297 0.0448493i
\(445\) 0.180247 0.554742i 0.00854451 0.0262973i
\(446\) −7.17041 + 22.0683i −0.339529 + 1.04496i
\(447\) 8.86693 6.44220i 0.419392 0.304706i
\(448\) 13.2639 + 9.63679i 0.626660 + 0.455295i
\(449\) 4.58174 + 14.1012i 0.216226 + 0.665475i 0.999064 + 0.0432498i \(0.0137711\pi\)
−0.782838 + 0.622225i \(0.786229\pi\)
\(450\) −1.47726 −0.0696387
\(451\) −5.80610 1.68488i −0.273399 0.0793380i
\(452\) −3.08001 −0.144872
\(453\) −6.19034 19.0519i −0.290848 0.895137i
\(454\) −1.75853 1.27765i −0.0825319 0.0599629i
\(455\) −3.97470 + 2.88779i −0.186337 + 0.135382i
\(456\) −1.81082 + 5.57314i −0.0847996 + 0.260986i
\(457\) 9.01788 27.7542i 0.421838 1.29829i −0.484151 0.874985i \(-0.660871\pi\)
0.905989 0.423301i \(-0.139129\pi\)
\(458\) −19.0922 + 13.8713i −0.892122 + 0.648165i
\(459\) −0.440466 0.320017i −0.0205592 0.0149371i
\(460\) 0.114867 + 0.353525i 0.00535571 + 0.0164832i
\(461\) −31.1798 −1.45219 −0.726094 0.687595i \(-0.758666\pi\)
−0.726094 + 0.687595i \(0.758666\pi\)
\(462\) −6.89440 8.88254i −0.320757 0.413253i
\(463\) 41.1642 1.91306 0.956531 0.291631i \(-0.0941978\pi\)
0.956531 + 0.291631i \(0.0941978\pi\)
\(464\) 13.3116 + 40.9689i 0.617976 + 1.90194i
\(465\) −5.47820 3.98015i −0.254046 0.184575i
\(466\) −30.6409 + 22.2619i −1.41941 + 1.03126i
\(467\) 11.9826 36.8788i 0.554490 1.70655i −0.142795 0.989752i \(-0.545609\pi\)
0.697285 0.716794i \(-0.254391\pi\)
\(468\) −0.120596 + 0.371156i −0.00557455 + 0.0171567i
\(469\) −18.1174 + 13.1630i −0.836582 + 0.607812i
\(470\) −0.451769 0.328230i −0.0208386 0.0151401i
\(471\) 2.82895 + 8.70662i 0.130351 + 0.401180i
\(472\) −21.6910 −0.998409
\(473\) 1.93675 0.697949i 0.0890518 0.0320917i
\(474\) 13.6270 0.625911
\(475\) −0.674367 2.07549i −0.0309421 0.0952299i
\(476\) 0.184276 + 0.133884i 0.00844626 + 0.00613656i
\(477\) −9.37901 + 6.81425i −0.429435 + 0.312003i
\(478\) 1.90911 5.87562i 0.0873205 0.268745i
\(479\) 5.15675 15.8708i 0.235618 0.725158i −0.761421 0.648258i \(-0.775498\pi\)
0.997039 0.0768997i \(-0.0245021\pi\)
\(480\) −0.831757 + 0.604307i −0.0379643 + 0.0275827i
\(481\) −15.2748 11.0978i −0.696473 0.506017i
\(482\) 1.50270 + 4.62483i 0.0684461 + 0.210655i
\(483\) −4.67961 −0.212930
\(484\) −0.497489 + 1.94258i −0.0226131 + 0.0882989i
\(485\) −5.37801 −0.244203
\(486\) −0.456498 1.40496i −0.0207072 0.0637302i
\(487\) −2.03220 1.47648i −0.0920877 0.0669056i 0.540789 0.841158i \(-0.318126\pi\)
−0.632876 + 0.774253i \(0.718126\pi\)
\(488\) −18.9562 + 13.7725i −0.858105 + 0.623450i
\(489\) −3.50181 + 10.7775i −0.158357 + 0.487373i
\(490\) 0.791178 2.43500i 0.0357418 0.110002i
\(491\) 6.11508 4.44286i 0.275970 0.200504i −0.441188 0.897415i \(-0.645443\pi\)
0.717158 + 0.696911i \(0.245443\pi\)
\(492\) 0.268833 + 0.195319i 0.0121199 + 0.00880565i
\(493\) −1.67325 5.14974i −0.0753594 0.231932i
\(494\) −6.90147 −0.310512
\(495\) −3.12020 + 1.12443i −0.140243 + 0.0505394i
\(496\) −29.3295 −1.31693
\(497\) 10.6354 + 32.7325i 0.477065 + 1.46825i
\(498\) −11.2967 8.20756i −0.506219 0.367789i
\(499\) −13.5886 + 9.87269i −0.608309 + 0.441962i −0.848818 0.528685i \(-0.822685\pi\)
0.240510 + 0.970647i \(0.422685\pi\)
\(500\) 0.0563329 0.173375i 0.00251928 0.00775356i
\(501\) 4.66619 14.3611i 0.208470 0.641605i
\(502\) −11.1919 + 8.13139i −0.499519 + 0.362922i
\(503\) −6.17489 4.48632i −0.275325 0.200035i 0.441551 0.897236i \(-0.354428\pi\)
−0.716876 + 0.697201i \(0.754428\pi\)
\(504\) −1.90431 5.86087i −0.0848248 0.261064i
\(505\) −19.5291 −0.869032
\(506\) 6.12569 + 7.89215i 0.272320 + 0.350849i
\(507\) −8.41709 −0.373816
\(508\) 0.232795 + 0.716469i 0.0103286 + 0.0317882i
\(509\) −26.6198 19.3404i −1.17990 0.857249i −0.187741 0.982219i \(-0.560117\pi\)
−0.992161 + 0.124970i \(0.960117\pi\)
\(510\) 0.650683 0.472749i 0.0288127 0.0209337i
\(511\) −5.57307 + 17.1521i −0.246538 + 0.758766i
\(512\) 5.81206 17.8877i 0.256859 0.790531i
\(513\) 1.76552 1.28272i 0.0779494 0.0566336i
\(514\) −15.0244 10.9159i −0.662699 0.481479i
\(515\) 4.01914 + 12.3697i 0.177105 + 0.545072i
\(516\) −0.113154 −0.00498133
\(517\) −1.20404 0.349403i −0.0529537 0.0153667i
\(518\) −29.9007 −1.31376
\(519\) 5.64392 + 17.3702i 0.247741 + 0.762467i
\(520\) 4.65059 + 3.37885i 0.203942 + 0.148173i
\(521\) −0.645559 + 0.469026i −0.0282824 + 0.0205484i −0.601837 0.798619i \(-0.705564\pi\)
0.573554 + 0.819168i \(0.305564\pi\)
\(522\) 4.54008 13.9729i 0.198714 0.611578i
\(523\) 1.33036 4.09443i 0.0581727 0.179037i −0.917748 0.397164i \(-0.869995\pi\)
0.975920 + 0.218127i \(0.0699945\pi\)
\(524\) 0.0643796 0.0467745i 0.00281244 0.00204336i
\(525\) 1.85666 + 1.34895i 0.0810315 + 0.0588728i
\(526\) −2.20464 6.78519i −0.0961270 0.295848i
\(527\) 3.68668 0.160594
\(528\) −8.07094 + 11.8839i −0.351242 + 0.517181i
\(529\) −18.8422 −0.819224
\(530\) −5.29223 16.2878i −0.229880 0.707497i
\(531\) 6.53518 + 4.74808i 0.283602 + 0.206049i
\(532\) −0.738630 + 0.536646i −0.0320237 + 0.0232666i
\(533\) 1.20586 3.71127i 0.0522318 0.160753i
\(534\) −0.266271 + 0.819498i −0.0115227 + 0.0354632i
\(535\) −1.59663 + 1.16002i −0.0690285 + 0.0501521i
\(536\) 21.1982 + 15.4014i 0.915623 + 0.665239i
\(537\) −0.162363 0.499703i −0.00700649 0.0215638i
\(538\) 7.72502 0.333049
\(539\) −0.182331 5.74530i −0.00785357 0.247468i
\(540\) 0.182297 0.00784482
\(541\) −7.01720 21.5967i −0.301693 0.928516i −0.980891 0.194560i \(-0.937672\pi\)
0.679198 0.733955i \(-0.262328\pi\)
\(542\) 36.2495 + 26.3368i 1.55705 + 1.13126i
\(543\) 14.3282 10.4101i 0.614883 0.446738i
\(544\) 0.172972 0.532353i 0.00741611 0.0228245i
\(545\) 3.28213 10.1014i 0.140591 0.432695i
\(546\) 5.87166 4.26601i 0.251284 0.182568i
\(547\) −26.0140 18.9003i −1.11228 0.808117i −0.129257 0.991611i \(-0.541259\pi\)
−0.983021 + 0.183494i \(0.941259\pi\)
\(548\) −0.443221 1.36409i −0.0189335 0.0582712i
\(549\) 8.72595 0.372415
\(550\) −0.155412 4.89705i −0.00662678 0.208811i
\(551\) 21.7039 0.924617
\(552\) 1.69198 + 5.20739i 0.0720156 + 0.221641i
\(553\) −17.1269 12.4434i −0.728309 0.529147i
\(554\) 19.0855 13.8665i 0.810867 0.589129i
\(555\) −2.72540 + 8.38793i −0.115687 + 0.356048i
\(556\) 0.993889 3.05888i 0.0421503 0.129725i
\(557\) −30.5122 + 22.1684i −1.29284 + 0.939306i −0.999859 0.0168116i \(-0.994648\pi\)
−0.292985 + 0.956117i \(0.594648\pi\)
\(558\) 8.09273 + 5.87971i 0.342593 + 0.248908i
\(559\) 0.410623 + 1.26377i 0.0173675 + 0.0534517i
\(560\) 9.94032 0.420055
\(561\) 1.01450 1.49379i 0.0428324 0.0630679i
\(562\) 2.05438 0.0866588
\(563\) 6.79438 + 20.9109i 0.286349 + 0.881291i 0.985991 + 0.166798i \(0.0533428\pi\)
−0.699642 + 0.714493i \(0.746657\pi\)
\(564\) 0.0557493 + 0.0405043i 0.00234747 + 0.00170554i
\(565\) 13.6688 9.93096i 0.575050 0.417799i
\(566\) −2.68171 + 8.25347i −0.112721 + 0.346919i
\(567\) −0.709183 + 2.18264i −0.0297829 + 0.0916622i
\(568\) 32.5788 23.6699i 1.36698 0.993166i
\(569\) 16.5690 + 12.0381i 0.694609 + 0.504663i 0.878172 0.478345i \(-0.158763\pi\)
−0.183563 + 0.983008i \(0.558763\pi\)
\(570\) 0.996215 + 3.06604i 0.0417269 + 0.128422i
\(571\) 17.4373 0.729728 0.364864 0.931061i \(-0.381116\pi\)
0.364864 + 0.931061i \(0.381116\pi\)
\(572\) −1.24305 0.360724i −0.0519747 0.0150826i
\(573\) −16.5519 −0.691467
\(574\) −1.90968 5.87739i −0.0797085 0.245317i
\(575\) −1.64965 1.19854i −0.0687951 0.0499826i
\(576\) −5.77957 + 4.19910i −0.240815 + 0.174963i
\(577\) −10.2701 + 31.6082i −0.427551 + 1.31587i 0.472978 + 0.881074i \(0.343179\pi\)
−0.900530 + 0.434794i \(0.856821\pi\)
\(578\) 7.62516 23.4678i 0.317165 0.976133i
\(579\) 19.8235 14.4026i 0.823838 0.598553i
\(580\) 1.46677 + 1.06567i 0.0609042 + 0.0442495i
\(581\) 6.70342 + 20.6310i 0.278105 + 0.855918i
\(582\) 7.94472 0.329319
\(583\) −23.5756 30.3741i −0.976403 1.25797i
\(584\) 21.1016 0.873192
\(585\) −0.661536 2.03600i −0.0273511 0.0841781i
\(586\) 23.8721 + 17.3441i 0.986147 + 0.716478i
\(587\) 34.6222 25.1545i 1.42901 1.03824i 0.438811 0.898580i \(-0.355400\pi\)
0.990200 0.139657i \(-0.0446001\pi\)
\(588\) −0.0976331 + 0.300484i −0.00402632 + 0.0123917i
\(589\) −4.56643 + 14.0540i −0.188156 + 0.579086i
\(590\) −9.65415 + 7.01415i −0.397455 + 0.288768i
\(591\) 6.07472 + 4.41354i 0.249881 + 0.181549i
\(592\) 11.8047 + 36.3312i 0.485171 + 1.49320i
\(593\) −42.6570 −1.75171 −0.875857 0.482570i \(-0.839703\pi\)
−0.875857 + 0.482570i \(0.839703\pi\)
\(594\) 4.60935 1.66108i 0.189124 0.0681548i
\(595\) −1.24948 −0.0512238
\(596\) −0.617416 1.90021i −0.0252903 0.0778357i
\(597\) 16.2577 + 11.8119i 0.665383 + 0.483429i
\(598\) −5.21698 + 3.79036i −0.213338 + 0.154999i
\(599\) 8.75148 26.9343i 0.357576 1.10051i −0.596925 0.802297i \(-0.703611\pi\)
0.954501 0.298208i \(-0.0963890\pi\)
\(600\) 0.829779 2.55380i 0.0338756 0.104258i
\(601\) 6.19268 4.49925i 0.252605 0.183528i −0.454276 0.890861i \(-0.650102\pi\)
0.706880 + 0.707333i \(0.250102\pi\)
\(602\) 1.70248 + 1.23692i 0.0693877 + 0.0504131i
\(603\) −3.01539 9.28043i −0.122796 0.377928i
\(604\) −3.65184 −0.148591
\(605\) −4.05569 10.2250i −0.164887 0.415707i
\(606\) 28.8495 1.17193
\(607\) 3.58415 + 11.0309i 0.145476 + 0.447730i 0.997072 0.0764693i \(-0.0243647\pi\)
−0.851596 + 0.524199i \(0.824365\pi\)
\(608\) 1.81514 + 1.31878i 0.0736137 + 0.0534835i
\(609\) −18.4653 + 13.4159i −0.748253 + 0.543638i
\(610\) −3.98338 + 12.2596i −0.161282 + 0.496376i
\(611\) 0.250066 0.769625i 0.0101166 0.0311357i
\(612\) −0.0802957 + 0.0583382i −0.00324576 + 0.00235818i
\(613\) 25.9757 + 18.8725i 1.04915 + 0.762251i 0.972050 0.234772i \(-0.0754344\pi\)
0.0770985 + 0.997023i \(0.475434\pi\)
\(614\) −8.87307 27.3085i −0.358088 1.10208i
\(615\) −1.82283 −0.0735035
\(616\) 19.2282 6.92929i 0.774725 0.279189i
\(617\) −18.7392 −0.754414 −0.377207 0.926129i \(-0.623115\pi\)
−0.377207 + 0.926129i \(0.623115\pi\)
\(618\) −5.93732 18.2732i −0.238834 0.735056i
\(619\) 31.6002 + 22.9589i 1.27012 + 0.922796i 0.999207 0.0398085i \(-0.0126748\pi\)
0.270912 + 0.962604i \(0.412675\pi\)
\(620\) −0.998661 + 0.725569i −0.0401072 + 0.0291396i
\(621\) 0.630110 1.93928i 0.0252854 0.0778205i
\(622\) −2.74895 + 8.46040i −0.110223 + 0.339231i
\(623\) 1.08297 0.786827i 0.0433884 0.0315236i
\(624\) −7.50158 5.45022i −0.300304 0.218183i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) 7.54633 0.301612
\(627\) 4.43790 + 5.71766i 0.177233 + 0.228341i
\(628\) 1.66887 0.0665952
\(629\) −1.48383 4.56677i −0.0591644 0.182089i
\(630\) −2.74278 1.99274i −0.109275 0.0793928i
\(631\) −36.4512 + 26.4833i −1.45110 + 1.05428i −0.465524 + 0.885035i \(0.654134\pi\)
−0.985573 + 0.169249i \(0.945866\pi\)
\(632\) −7.65433 + 23.5576i −0.304473 + 0.937071i
\(633\) 1.67444 5.15339i 0.0665530 0.204829i
\(634\) 16.3479 11.8775i 0.649260 0.471715i
\(635\) −3.34325 2.42901i −0.132673 0.0963924i
\(636\) 0.653073 + 2.00995i 0.0258960 + 0.0796997i
\(637\) 3.71027 0.147006
\(638\) 46.7972 + 13.5802i 1.85272 + 0.537644i
\(639\) −14.9968 −0.593263
\(640\) −3.89660 11.9925i −0.154027 0.474046i
\(641\) −20.9477 15.2194i −0.827384 0.601130i 0.0914341 0.995811i \(-0.470855\pi\)
−0.918818 + 0.394682i \(0.870855\pi\)
\(642\) 2.35864 1.71365i 0.0930882 0.0676325i
\(643\) 9.46770 29.1386i 0.373370 1.14911i −0.571202 0.820809i \(-0.693523\pi\)
0.944572 0.328304i \(-0.106477\pi\)
\(644\) −0.263616 + 0.811326i −0.0103879 + 0.0319707i
\(645\) 0.502167 0.364846i 0.0197728 0.0143658i
\(646\) −1.41998 1.03168i −0.0558685 0.0405908i
\(647\) −4.66875 14.3689i −0.183547 0.564901i 0.816373 0.577525i \(-0.195981\pi\)
−0.999920 + 0.0126243i \(0.995981\pi\)
\(648\) 2.68522 0.105485
\(649\) −15.0522 + 22.1633i −0.590849 + 0.869987i
\(650\) 3.16248 0.124043
\(651\) −4.80218 14.7796i −0.188212 0.579258i
\(652\) 1.67127 + 1.21425i 0.0654521 + 0.0475537i
\(653\) 4.23543 3.07722i 0.165745 0.120421i −0.501821 0.864972i \(-0.667336\pi\)
0.667566 + 0.744551i \(0.267336\pi\)
\(654\) −4.84856 + 14.9223i −0.189594 + 0.583510i
\(655\) −0.134894 + 0.415162i −0.00527075 + 0.0162217i
\(656\) −6.38745 + 4.64075i −0.249388 + 0.181191i
\(657\) −6.35761 4.61907i −0.248034 0.180207i
\(658\) −0.396020 1.21882i −0.0154385 0.0475147i
\(659\) 14.9207 0.581229 0.290615 0.956840i \(-0.406140\pi\)
0.290615 + 0.956840i \(0.406140\pi\)
\(660\) 0.0191781 + 0.604307i 0.000746508 + 0.0235226i
\(661\) 45.7403 1.77909 0.889545 0.456847i \(-0.151021\pi\)
0.889545 + 0.456847i \(0.151021\pi\)
\(662\) −5.23579 16.1141i −0.203495 0.626292i
\(663\) 0.942938 + 0.685085i 0.0366207 + 0.0266065i
\(664\) 20.5341 14.9189i 0.796878 0.578966i
\(665\) 1.54765 4.76317i 0.0600152 0.184708i
\(666\) 4.02613 12.3912i 0.156009 0.480147i
\(667\) 16.4065 11.9200i 0.635261 0.461544i
\(668\) −2.22699 1.61800i −0.0861647 0.0626023i
\(669\) 4.85386 + 14.9386i 0.187661 + 0.577561i
\(670\) 14.4151 0.556905
\(671\) 0.917993 + 28.9261i 0.0354387 + 1.11668i
\(672\) −2.35947 −0.0910185
\(673\) 6.52294 + 20.0755i 0.251441 + 0.773855i 0.994510 + 0.104641i \(0.0333693\pi\)
−0.743069 + 0.669214i \(0.766631\pi\)
\(674\) 4.49852 + 3.26836i 0.173276 + 0.125893i
\(675\) −0.809017 + 0.587785i −0.0311391 + 0.0226239i
\(676\) −0.474159 + 1.45931i −0.0182369 + 0.0561273i
\(677\) −13.6182 + 41.9125i −0.523390 + 1.61083i 0.244087 + 0.969753i \(0.421512\pi\)
−0.767477 + 0.641077i \(0.778488\pi\)
\(678\) −20.1924 + 14.6706i −0.775483 + 0.563421i
\(679\) −9.98516 7.25464i −0.383195 0.278408i
\(680\) 0.451769 + 1.39040i 0.0173246 + 0.0533195i
\(681\) −1.47141 −0.0563847
\(682\) −18.6396 + 27.4456i −0.713748 + 1.05095i
\(683\) −42.5318 −1.62743 −0.813717 0.581261i \(-0.802560\pi\)
−0.813717 + 0.581261i \(0.802560\pi\)
\(684\) −0.122935 0.378355i −0.00470054 0.0144668i
\(685\) 6.36526 + 4.62463i 0.243204 + 0.176698i
\(686\) 23.9531 17.4029i 0.914532 0.664446i
\(687\) −4.93656 + 15.1932i −0.188342 + 0.579656i
\(688\) 0.830802 2.55694i 0.0316740 0.0974826i
\(689\) 20.0783 14.5878i 0.764924 0.555750i
\(690\) 2.43696 + 1.77055i 0.0927735 + 0.0674039i
\(691\) −1.77552 5.46449i −0.0675439 0.207879i 0.911588 0.411105i \(-0.134857\pi\)
−0.979132 + 0.203227i \(0.934857\pi\)
\(692\) 3.32949 0.126568
\(693\) −7.30996 2.12129i −0.277682 0.0805811i
\(694\) 0.584966 0.0222050
\(695\) 5.45203 + 16.7796i 0.206807 + 0.636487i
\(696\) 21.6054 + 15.6972i 0.818949 + 0.595001i
\(697\) 0.802893 0.583336i 0.0304117 0.0220954i
\(698\) 6.01244 18.5044i 0.227574 0.700401i
\(699\) −7.92263 + 24.3833i −0.299661 + 0.922263i
\(700\) 0.338464 0.245909i 0.0127928 0.00929448i
\(701\) 0.983718 + 0.714713i 0.0371545 + 0.0269943i 0.606208 0.795307i \(-0.292690\pi\)
−0.569053 + 0.822301i \(0.692690\pi\)
\(702\) 0.977260 + 3.00770i 0.0368843 + 0.113518i
\(703\) 19.2470 0.725913
\(704\) −14.5279 18.7173i −0.547540 0.705433i
\(705\) −0.378009 −0.0142366
\(706\) −5.19736 15.9958i −0.195605 0.602011i
\(707\) −36.2589 26.3437i −1.36366 0.990755i
\(708\) 1.19134 0.865562i 0.0447734 0.0325298i
\(709\) −8.16115 + 25.1174i −0.306498 + 0.943305i 0.672615 + 0.739992i \(0.265171\pi\)
−0.979114 + 0.203313i \(0.934829\pi\)
\(710\) 6.84600 21.0698i 0.256926 0.790736i
\(711\) 7.46281 5.42205i 0.279877 0.203343i
\(712\) −1.26713 0.920626i −0.0474878 0.0345019i
\(713\) 4.26675 + 13.1317i 0.159791 + 0.491786i
\(714\) 1.84581 0.0690777
\(715\) 6.67965 2.40715i 0.249805 0.0900224i
\(716\) −0.0957823 −0.00357955
\(717\) −1.29233 3.97738i −0.0482629 0.148538i
\(718\) −17.1719 12.4761i −0.640849 0.465604i
\(719\) −40.0007 + 29.0622i −1.49177 + 1.08384i −0.518255 + 0.855226i \(0.673418\pi\)
−0.973518 + 0.228611i \(0.926582\pi\)
\(720\) −1.33846 + 4.11937i −0.0498816 + 0.153520i
\(721\) −9.22379 + 28.3879i −0.343512 + 1.05722i
\(722\) −17.0157 + 12.3627i −0.633260 + 0.460090i
\(723\) 2.66312 + 1.93487i 0.0990425 + 0.0719586i
\(724\) −0.997692 3.07058i −0.0370789 0.114117i
\(725\) −9.94544 −0.369364
\(726\) 5.99131 + 15.1050i 0.222359 + 0.560600i
\(727\) −39.2447 −1.45551 −0.727753 0.685839i \(-0.759435\pi\)
−0.727753 + 0.685839i \(0.759435\pi\)
\(728\) 4.07670 + 12.5468i 0.151093 + 0.465015i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 9.39184 6.82357i 0.347608 0.252552i
\(731\) −0.104431 + 0.321404i −0.00386250 + 0.0118876i
\(732\) 0.491558 1.51286i 0.0181685 0.0559169i
\(733\) −4.20624 + 3.05601i −0.155361 + 0.112876i −0.662750 0.748841i \(-0.730611\pi\)
0.507389 + 0.861717i \(0.330611\pi\)
\(734\) −31.3888 22.8053i −1.15858 0.841760i
\(735\) −0.535571 1.64832i −0.0197548 0.0607992i
\(736\) 2.09639 0.0772740
\(737\) 30.4470 10.9722i 1.12153 0.404167i
\(738\) 2.69279 0.0991229
\(739\) 8.96428 + 27.5892i 0.329757 + 1.01489i 0.969248 + 0.246088i \(0.0791451\pi\)
−0.639491 + 0.768799i \(0.720855\pi\)
\(740\) 1.30073 + 0.945033i 0.0478156 + 0.0347401i
\(741\) −3.77957 + 2.74602i −0.138846 + 0.100877i
\(742\) 12.1455 37.3799i 0.445874 1.37226i
\(743\) 2.62874 8.09042i 0.0964390 0.296809i −0.891187 0.453636i \(-0.850127\pi\)
0.987626 + 0.156827i \(0.0501266\pi\)
\(744\) −14.7102 + 10.6876i −0.539301 + 0.391825i
\(745\) 8.86693 + 6.44220i 0.324859 + 0.236024i
\(746\) −9.99506 30.7616i −0.365945 1.12626i
\(747\) −9.45232 −0.345842
\(748\) −0.201836 0.260039i −0.00737985 0.00950798i
\(749\) −4.52922 −0.165494
\(750\) −0.456498 1.40496i −0.0166690 0.0513018i
\(751\) 28.4006 + 20.6343i 1.03635 + 0.752955i 0.969570 0.244813i \(-0.0787264\pi\)
0.0667831 + 0.997768i \(0.478726\pi\)
\(752\) −1.32460 + 0.962377i −0.0483032 + 0.0350943i
\(753\) −2.89382 + 8.90626i −0.105457 + 0.324562i
\(754\) −9.71928 + 29.9129i −0.353955 + 1.08936i
\(755\) 16.2065 11.7747i 0.589816 0.428526i
\(756\) 0.338464 + 0.245909i 0.0123098 + 0.00894362i
\(757\) −2.21972 6.83159i −0.0806771 0.248298i 0.902580 0.430522i \(-0.141671\pi\)
−0.983257 + 0.182224i \(0.941671\pi\)
\(758\) −37.7582 −1.37144
\(759\) 6.49491 + 1.88477i 0.235750 + 0.0684128i
\(760\) −5.85995 −0.212563
\(761\) −13.4072 41.2631i −0.486011 1.49579i −0.830512 0.557001i \(-0.811952\pi\)
0.344501 0.938786i \(-0.388048\pi\)
\(762\) 4.93885 + 3.58828i 0.178916 + 0.129990i
\(763\) 19.7200 14.3274i 0.713912 0.518687i
\(764\) −0.932419 + 2.86969i −0.0337337 + 0.103822i
\(765\) 0.168243 0.517799i 0.00608284 0.0187211i
\(766\) 22.7695 16.5430i 0.822696 0.597724i
\(767\) −13.9903 10.1646i −0.505162 0.367021i
\(768\) 1.34110 + 4.12748i 0.0483927 + 0.148937i
\(769\) −19.6548 −0.708771 −0.354385 0.935099i \(-0.615310\pi\)
−0.354385 + 0.935099i \(0.615310\pi\)
\(770\) 6.31731 9.30182i 0.227660 0.335214i
\(771\) −12.5714 −0.452747
\(772\) −1.38034 4.24824i −0.0496795 0.152898i
\(773\) 19.7691 + 14.3631i 0.711044 + 0.516604i 0.883510 0.468412i \(-0.155174\pi\)
−0.172466 + 0.985015i \(0.555174\pi\)
\(774\) −0.741831 + 0.538972i −0.0266646 + 0.0193729i
\(775\) 2.09249 6.44002i 0.0751644 0.231332i
\(776\) −4.46256 + 13.7343i −0.160196 + 0.493034i
\(777\) −16.3750 + 11.8971i −0.587450 + 0.426808i
\(778\) 19.5912 + 14.2338i 0.702377 + 0.510307i
\(779\) 1.22925 + 3.78326i 0.0440426 + 0.135549i
\(780\) −0.390257 −0.0139734
\(781\) −1.57770 49.7136i −0.0564545 1.77889i
\(782\) −1.64001 −0.0586465
\(783\) −3.07331 9.45867i −0.109831 0.338025i
\(784\) −6.07319 4.41243i −0.216900 0.157587i
\(785\) −7.40629 + 5.38098i −0.264342 + 0.192056i
\(786\) 0.199274 0.613302i 0.00710786 0.0218758i
\(787\) −10.5508 + 32.4721i −0.376096 + 1.15750i 0.566640 + 0.823965i \(0.308243\pi\)
−0.942736 + 0.333539i \(0.891757\pi\)
\(788\) 1.10740 0.804576i 0.0394496 0.0286618i
\(789\) −3.90712 2.83869i −0.139097 0.101060i
\(790\) 4.21099 + 12.9601i 0.149820 + 0.461099i
\(791\) 38.7747 1.37867
\(792\) 0.282492 + 8.90139i 0.0100379 + 0.316297i
\(793\) −18.6803 −0.663357
\(794\) −14.1435 43.5292i −0.501934 1.54479i
\(795\) −9.37901 6.81425i −0.332639 0.241677i
\(796\) 2.96373 2.15327i 0.105047 0.0763208i
\(797\) −0.940349 + 2.89410i −0.0333089 + 0.102514i −0.966329 0.257311i \(-0.917164\pi\)
0.933020 + 0.359825i \(0.117164\pi\)
\(798\) −2.28628 + 7.03644i −0.0809333 + 0.249087i
\(799\) 0.166500 0.120969i 0.00589035 0.00427959i
\(800\) −0.831757 0.604307i −0.0294071 0.0213655i
\(801\) 0.180247 + 0.554742i 0.00636870 + 0.0196008i
\(802\) 9.40439 0.332081
\(803\) 14.6432 21.5611i 0.516747 0.760876i
\(804\) −1.77886 −0.0627355
\(805\) −1.44608 4.45057i −0.0509676 0.156862i
\(806\) −17.3247 12.5871i −0.610237 0.443363i
\(807\) 4.23058 3.07370i 0.148924 0.108199i
\(808\) −16.2048 + 49.8733i −0.570083 + 1.75454i
\(809\) −3.43043 + 10.5578i −0.120607 + 0.371191i −0.993075 0.117480i \(-0.962518\pi\)
0.872468 + 0.488672i \(0.162518\pi\)
\(810\) 1.19513 0.868312i 0.0419925 0.0305094i
\(811\) −33.4336 24.2909i −1.17401 0.852969i −0.182528 0.983201i \(-0.558428\pi\)
−0.991484 + 0.130231i \(0.958428\pi\)
\(812\) 1.28577 + 3.95718i 0.0451215 + 0.138870i
\(813\) 30.3311 1.06376
\(814\) 41.4997 + 12.0429i 1.45456 + 0.422102i
\(815\) −11.3321 −0.396946
\(816\) −0.728721 2.24277i −0.0255103 0.0785128i
\(817\) −1.09588 0.796202i −0.0383399 0.0278556i
\(818\) −7.49195 + 5.44322i −0.261950 + 0.190318i
\(819\) 1.51820 4.67254i 0.0530502 0.163272i
\(820\) −0.102685 + 0.316032i −0.00358592 + 0.0110363i
\(821\) −6.61681 + 4.80739i −0.230928 + 0.167779i −0.697232 0.716845i \(-0.745585\pi\)
0.466304 + 0.884625i \(0.345585\pi\)
\(822\) −9.40314 6.83178i −0.327972 0.238286i
\(823\) 4.07819 + 12.5514i 0.142157 + 0.437513i 0.996634 0.0819748i \(-0.0261227\pi\)
−0.854478 + 0.519488i \(0.826123\pi\)
\(824\) 34.9246 1.21665
\(825\) −2.03359 2.62002i −0.0708006 0.0912174i
\(826\) −27.3862 −0.952889
\(827\) −9.49825 29.2326i −0.330287 1.01652i −0.968997 0.247071i \(-0.920532\pi\)
0.638711 0.769447i \(-0.279468\pi\)
\(828\) −0.300726 0.218490i −0.0104510 0.00759306i
\(829\) −2.98357 + 2.16769i −0.103624 + 0.0752871i −0.638390 0.769713i \(-0.720399\pi\)
0.534767 + 0.845000i \(0.320399\pi\)
\(830\) 4.31497 13.2801i 0.149775 0.460959i
\(831\) 4.93483 15.1878i 0.171187 0.526861i
\(832\) 12.3728 8.98933i 0.428948 0.311649i
\(833\) 0.763391 + 0.554636i 0.0264499 + 0.0192170i
\(834\) −8.05407 24.7879i −0.278889 0.858334i
\(835\) 15.1001 0.522561
\(836\) 1.24130 0.447329i 0.0429312 0.0154712i
\(837\) 6.77143 0.234055
\(838\) −1.78186 5.48399i −0.0615533 0.189441i
\(839\) −35.2341 25.5991i −1.21642 0.883778i −0.220618 0.975360i \(-0.570808\pi\)
−0.995798 + 0.0915823i \(0.970808\pi\)
\(840\) 4.98555 3.62221i 0.172018 0.124978i
\(841\) 21.6039 66.4900i 0.744963 2.29276i
\(842\) −7.93008 + 24.4063i −0.273289 + 0.841096i
\(843\) 1.12508 0.817415i 0.0387497 0.0281533i
\(844\) −0.799143 0.580611i −0.0275076 0.0199855i
\(845\) −2.60102 8.00513i −0.0894779 0.275385i
\(846\) 0.558418 0.0191988
\(847\) 6.26295 24.4554i 0.215198 0.840296i
\(848\) −50.2139 −1.72435
\(849\) 1.81533 + 5.58701i 0.0623019 + 0.191746i
\(850\) 0.650683 + 0.472749i 0.0223182 + 0.0162151i
\(851\) 14.5492 10.5706i 0.498741 0.362357i
\(852\) −0.844811 + 2.60006i −0.0289428 + 0.0890766i
\(853\) −9.37662 + 28.8583i −0.321049 + 0.988088i 0.652143 + 0.758096i \(0.273870\pi\)
−0.973192 + 0.229992i \(0.926130\pi\)
\(854\) −23.9333 + 17.3886i −0.818982 + 0.595025i
\(855\) 1.76552 + 1.28272i 0.0603794 + 0.0438682i
\(856\) 1.63761 + 5.04004i 0.0559723 + 0.172265i
\(857\) 12.5402 0.428365 0.214182 0.976794i \(-0.431291\pi\)
0.214182 + 0.976794i \(0.431291\pi\)
\(858\) −9.86757 + 3.55599i −0.336873 + 0.121400i
\(859\) −8.67783 −0.296084 −0.148042 0.988981i \(-0.547297\pi\)
−0.148042 + 0.988981i \(0.547297\pi\)
\(860\) −0.0349665 0.107616i −0.00119235 0.00366967i
\(861\) −3.38438 2.45889i −0.115339 0.0837989i
\(862\) −8.40953 + 6.10988i −0.286430 + 0.208103i
\(863\) −11.8637 + 36.5128i −0.403846 + 1.24291i 0.518009 + 0.855375i \(0.326673\pi\)
−0.921855 + 0.387535i \(0.873327\pi\)
\(864\) 0.317703 0.977789i 0.0108085 0.0332651i
\(865\) −14.7760 + 10.7354i −0.502398 + 0.365014i
\(866\) 3.28935 + 2.38985i 0.111777 + 0.0812104i
\(867\) −5.16169 15.8860i −0.175300 0.539518i
\(868\) −2.83293 −0.0961559
\(869\) 18.7590 + 24.1685i 0.636354 + 0.819859i
\(870\) 14.6920 0.498105
\(871\) 6.45528 + 19.8673i 0.218729 + 0.673178i
\(872\) −23.0734 16.7638i −0.781363 0.567693i
\(873\) 4.35090 3.16111i 0.147256 0.106988i
\(874\) 2.03136 6.25188i 0.0687118 0.211473i
\(875\) −0.709183 + 2.18264i −0.0239747 + 0.0737867i
\(876\) −1.15897 + 0.842044i −0.0391581 + 0.0284500i
\(877\) −25.3140 18.3917i −0.854792 0.621043i 0.0716708 0.997428i \(-0.477167\pi\)
−0.926463 + 0.376385i \(0.877167\pi\)
\(878\) 1.24945 + 3.84542i 0.0421669 + 0.129777i
\(879\) 19.9745 0.673723
\(880\) −13.7963 4.00358i −0.465075 0.134961i
\(881\) 49.2703 1.65996 0.829979 0.557795i \(-0.188353\pi\)
0.829979 + 0.557795i \(0.188353\pi\)
\(882\) 0.791178 + 2.43500i 0.0266404 + 0.0819906i
\(883\) −22.8031 16.5674i −0.767385 0.557537i 0.133782 0.991011i \(-0.457288\pi\)
−0.901166 + 0.433473i \(0.857288\pi\)
\(884\) 0.171895 0.124889i 0.00578145 0.00420047i
\(885\) −2.49622 + 7.68256i −0.0839094 + 0.258246i
\(886\) −5.06905 + 15.6009i −0.170298 + 0.524123i
\(887\) 20.6253 14.9852i 0.692531 0.503153i −0.184960 0.982746i \(-0.559216\pi\)
0.877491 + 0.479593i \(0.159216\pi\)
\(888\) 19.1596 + 13.9202i 0.642953 + 0.467133i
\(889\) −2.93068 9.01972i −0.0982920 0.302512i
\(890\) −0.861672 −0.0288833
\(891\) 1.86337 2.74369i 0.0624253 0.0919171i
\(892\) 2.86342 0.0958743
\(893\) 0.254917 + 0.784553i 0.00853047 + 0.0262541i
\(894\) −13.0988 9.51681i −0.438088 0.318290i
\(895\) 0.425073 0.308833i 0.0142086 0.0103232i
\(896\) 8.94256 27.5224i 0.298750 0.919458i
\(897\) −1.34892 + 4.15156i −0.0450392 + 0.138616i
\(898\) 17.7200 12.8743i 0.591323 0.429621i
\(899\) 54.4831 + 39.5843i 1.81711 + 1.32021i
\(900\) 0.0563329 + 0.173375i 0.00187776 + 0.00577916i
\(901\) 6.31181 0.210277
\(902\) 0.283289 + 8.92648i 0.00943248 + 0.297219i
\(903\) 1.42451 0.0474048
\(904\) −14.0196 43.1478i −0.466284 1.43507i
\(905\) 14.3282 + 10.4101i 0.476286 + 0.346042i
\(906\) −23.9413 + 17.3943i −0.795395 + 0.577888i
\(907\) 0.766528 2.35913i 0.0254522 0.0783337i −0.937524 0.347922i \(-0.886888\pi\)
0.962976 + 0.269588i \(0.0868875\pi\)
\(908\) −0.0828891 + 0.255106i −0.00275077 + 0.00846600i
\(909\) 15.7994 11.4789i 0.524031 0.380731i
\(910\) 5.87166 + 4.26601i 0.194644 + 0.141417i
\(911\) 0.839165 + 2.58268i 0.0278028 + 0.0855681i 0.963995 0.265920i \(-0.0856757\pi\)
−0.936192 + 0.351488i \(0.885676\pi\)
\(912\) 9.45232 0.312998
\(913\) −0.994409 31.3340i −0.0329101 1.03700i
\(914\) −43.1101 −1.42595
\(915\) 2.69647 + 8.29887i 0.0891425 + 0.274352i
\(916\) 2.35602 + 1.71175i 0.0778453 + 0.0565579i
\(917\) −0.810484 + 0.588851i −0.0267645 + 0.0194456i
\(918\) −0.248539 + 0.764923i −0.00820300 + 0.0252462i
\(919\) 1.00091 3.08047i 0.0330169 0.101615i −0.933190 0.359383i \(-0.882987\pi\)
0.966207 + 0.257768i \(0.0829870\pi\)
\(920\) −4.42967 + 3.21834i −0.146042 + 0.106106i
\(921\) −15.7251 11.4249i −0.518158 0.376464i
\(922\) 14.2335 + 43.8063i 0.468757 + 1.44268i
\(923\) 32.1047 1.05674
\(924\) −0.779570 + 1.14786i −0.0256460 + 0.0377620i
\(925\) −8.81959 −0.289986
\(926\) −18.7914 57.8339i −0.617523 1.90054i
\(927\) −10.5223 7.64487i −0.345596 0.251090i
\(928\) 8.27219 6.01010i 0.271548 0.197291i
\(929\) 2.21938 6.83056i 0.0728156 0.224103i −0.908025 0.418916i \(-0.862410\pi\)
0.980840 + 0.194813i \(0.0624100\pi\)
\(930\) −3.09115 + 9.51358i −0.101363 + 0.311962i
\(931\) −3.05989 + 2.22314i −0.100284 + 0.0728606i
\(932\) 3.78115 + 2.74717i 0.123856 + 0.0899865i
\(933\) 1.86084 + 5.72709i 0.0609213 + 0.187496i
\(934\) −57.2832 −1.87436
\(935\) 1.73418 + 0.503244i 0.0567137 + 0.0164578i
\(936\) −5.74845 −0.187894
\(937\) 6.27696 + 19.3185i 0.205059 + 0.631108i 0.999711 + 0.0240421i \(0.00765359\pi\)
−0.794652 + 0.607066i \(0.792346\pi\)
\(938\) 26.7641 + 19.4452i 0.873877 + 0.634909i
\(939\) 4.13273 3.00260i 0.134866 0.0979862i
\(940\) −0.0212943 + 0.0655373i −0.000694545 + 0.00213759i
\(941\) −7.85663 + 24.1802i −0.256119 + 0.788253i 0.737488 + 0.675360i \(0.236012\pi\)
−0.993607 + 0.112893i \(0.963988\pi\)
\(942\) 10.9410 7.94911i 0.356478 0.258996i
\(943\) 3.00702 + 2.18473i 0.0979222 + 0.0711446i
\(944\) 10.8120 + 33.2760i 0.351901 + 1.08304i
\(945\) −2.29496 −0.0746551
\(946\) −1.86471 2.40244i −0.0606270 0.0781099i
\(947\) −4.55536 −0.148029 −0.0740147 0.997257i \(-0.523581\pi\)
−0.0740147 + 0.997257i \(0.523581\pi\)
\(948\) −0.519645 1.59930i −0.0168773 0.0519430i
\(949\) 13.6102 + 9.88839i 0.441806 + 0.320991i
\(950\) −2.60813 + 1.89491i −0.0846188 + 0.0614791i
\(951\) 4.22699 13.0093i 0.137069 0.421856i
\(952\) −1.03679 + 3.19092i −0.0336027 + 0.103418i
\(953\) 33.6433 24.4433i 1.08981 0.791797i 0.110447 0.993882i \(-0.464772\pi\)
0.979368 + 0.202085i \(0.0647718\pi\)
\(954\) 13.8552 + 10.0664i 0.448580 + 0.325912i
\(955\) −5.11483 15.7418i −0.165512 0.509394i
\(956\) −0.762378 −0.0246571
\(957\) 31.0318 11.1830i 1.00311 0.361494i
\(958\) −24.6519 −0.796467
\(959\) 5.57977 + 17.1728i 0.180180 + 0.554538i
\(960\) −5.77957 4.19910i −0.186535 0.135525i
\(961\) −12.0158 + 8.72996i −0.387605 + 0.281612i
\(962\) −8.61903 + 26.5267i −0.277889 + 0.855254i
\(963\) 0.609860 1.87695i 0.0196525 0.0604840i
\(964\) 0.485479 0.352721i 0.0156362 0.0113604i
\(965\) 19.8235 + 14.4026i 0.638142 + 0.463637i
\(966\) 2.13623 + 6.57465i 0.0687322 + 0.211536i
\(967\) −16.2161 −0.521476 −0.260738 0.965410i \(-0.583966\pi\)
−0.260738 + 0.965410i \(0.583966\pi\)
\(968\) −29.4780 + 1.87290i −0.947458 + 0.0601972i
\(969\) −1.18814 −0.0381686
\(970\) 2.45505 + 7.55588i 0.0788270 + 0.242605i
\(971\) 10.8979 + 7.91778i 0.349730 + 0.254094i 0.748756 0.662846i \(-0.230652\pi\)
−0.399026 + 0.916940i \(0.630652\pi\)
\(972\) −0.147481 + 0.107152i −0.00473047 + 0.00343689i
\(973\) −12.5122 + 38.5086i −0.401123 + 1.23453i
\(974\) −1.14669 + 3.52916i −0.0367425 + 0.113082i
\(975\) 1.73192 1.25832i 0.0554659 0.0402983i
\(976\) 30.5770 + 22.2155i 0.978746 + 0.711101i
\(977\) −4.49311 13.8284i −0.143747 0.442409i 0.853100 0.521747i \(-0.174719\pi\)
−0.996848 + 0.0793377i \(0.974719\pi\)
\(978\) 16.7404 0.535300
\(979\) −1.81998 + 0.655870i −0.0581669 + 0.0209617i
\(980\) −0.315947 −0.0100926
\(981\) 3.28213 + 10.1014i 0.104790 + 0.322512i
\(982\) −9.03356 6.56326i −0.288272 0.209442i
\(983\) 19.8968 14.4559i 0.634611 0.461072i −0.223384 0.974731i \(-0.571710\pi\)
0.857994 + 0.513659i \(0.171710\pi\)
\(984\) −1.51254 + 4.65513i −0.0482181 + 0.148400i
\(985\) −2.32034 + 7.14126i −0.0739321 + 0.227540i
\(986\) −6.47132 + 4.70169i −0.206089 + 0.149732i
\(987\) −0.701836 0.509914i −0.0223397 0.0162307i
\(988\) 0.263176 + 0.809973i 0.00837275 + 0.0257687i
\(989\) −1.26568 −0.0402463
\(990\) 3.00415 + 3.87045i 0.0954780 + 0.123011i
\(991\) 4.43775 0.140970 0.0704848 0.997513i \(-0.477545\pi\)
0.0704848 + 0.997513i \(0.477545\pi\)
\(992\) 2.15130 + 6.62103i 0.0683040 + 0.210218i
\(993\) −9.27899 6.74158i −0.294460 0.213938i
\(994\) 41.1328 29.8847i 1.30465 0.947885i
\(995\) −6.20988 + 19.1121i −0.196867 + 0.605893i
\(996\) −0.532477 + 1.63879i −0.0168722 + 0.0519272i
\(997\) −0.00847083 + 0.00615442i −0.000268274 + 0.000194912i −0.587919 0.808920i \(-0.700053\pi\)
0.587651 + 0.809114i \(0.300053\pi\)
\(998\) 20.0739 + 14.5845i 0.635427 + 0.461665i
\(999\) −2.72540 8.38793i −0.0862280 0.265382i
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 165.2.m.d.16.1 8
3.2 odd 2 495.2.n.a.181.2 8
5.2 odd 4 825.2.bx.f.49.4 16
5.3 odd 4 825.2.bx.f.49.1 16
5.4 even 2 825.2.n.g.676.2 8
11.3 even 5 1815.2.a.p.1.2 4
11.8 odd 10 1815.2.a.w.1.3 4
11.9 even 5 inner 165.2.m.d.31.1 yes 8
33.8 even 10 5445.2.a.bf.1.2 4
33.14 odd 10 5445.2.a.bt.1.3 4
33.20 odd 10 495.2.n.a.361.2 8
55.9 even 10 825.2.n.g.526.2 8
55.14 even 10 9075.2.a.di.1.3 4
55.19 odd 10 9075.2.a.cm.1.2 4
55.42 odd 20 825.2.bx.f.724.1 16
55.53 odd 20 825.2.bx.f.724.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.d.16.1 8 1.1 even 1 trivial
165.2.m.d.31.1 yes 8 11.9 even 5 inner
495.2.n.a.181.2 8 3.2 odd 2
495.2.n.a.361.2 8 33.20 odd 10
825.2.n.g.526.2 8 55.9 even 10
825.2.n.g.676.2 8 5.4 even 2
825.2.bx.f.49.1 16 5.3 odd 4
825.2.bx.f.49.4 16 5.2 odd 4
825.2.bx.f.724.1 16 55.42 odd 20
825.2.bx.f.724.4 16 55.53 odd 20
1815.2.a.p.1.2 4 11.3 even 5
1815.2.a.w.1.3 4 11.8 odd 10
5445.2.a.bf.1.2 4 33.8 even 10
5445.2.a.bt.1.3 4 33.14 odd 10
9075.2.a.cm.1.2 4 55.19 odd 10
9075.2.a.di.1.3 4 55.14 even 10