Properties

Label 21.3.h.b.11.1
Level $21$
Weight $3$
Character 21.11
Analytic conductor $0.572$
Analytic rank $0$
Dimension $4$
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] = [21,3,Mod(2,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 21.h (of order \(6\), 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: \(0.572208555157\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 5x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-1.93649 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 21.11
Dual form 21.3.h.b.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.93649 + 1.11803i) q^{2} +(0.936492 + 2.85008i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.00000 - 4.47214i) q^{6} +(3.50000 - 6.06218i) q^{7} -6.70820i q^{8} +(-7.24597 + 5.33816i) q^{9} +O(q^{10})\) \(q+(-1.93649 + 1.11803i) q^{2} +(0.936492 + 2.85008i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.00000 - 4.47214i) q^{6} +(3.50000 - 6.06218i) q^{7} -6.70820i q^{8} +(-7.24597 + 5.33816i) q^{9} +(-2.50000 + 4.33013i) q^{10} +(9.68246 + 5.59017i) q^{11} +(2.93649 + 0.614017i) q^{12} -2.00000 q^{13} +15.6525i q^{14} +(5.00000 + 4.47214i) q^{15} +(9.50000 + 16.4545i) q^{16} +(-23.2379 - 13.4164i) q^{17} +(8.06351 - 18.4385i) q^{18} +(-8.00000 - 13.8564i) q^{19} -2.23607i q^{20} +(20.5554 + 4.29812i) q^{21} -25.0000 q^{22} +(11.6190 - 6.70820i) q^{23} +(19.1190 - 6.28218i) q^{24} +(-10.0000 + 17.3205i) q^{25} +(3.87298 - 2.23607i) q^{26} +(-22.0000 - 15.6525i) q^{27} +(-3.50000 - 6.06218i) q^{28} +15.6525i q^{29} +(-14.6825 - 3.07008i) q^{30} +(1.50000 - 2.59808i) q^{31} +(-13.5554 - 7.82624i) q^{32} +(-6.86492 + 32.8310i) q^{33} +60.0000 q^{34} -15.6525i q^{35} +(1.00000 + 8.94427i) q^{36} +(-6.00000 - 10.3923i) q^{37} +(30.9839 + 17.8885i) q^{38} +(-1.87298 - 5.70017i) q^{39} +(-7.50000 - 12.9904i) q^{40} +31.3050i q^{41} +(-44.6109 + 14.6584i) q^{42} +44.0000 q^{43} +(9.68246 - 5.59017i) q^{44} +(-8.06351 + 18.4385i) q^{45} +(-15.0000 + 25.9808i) q^{46} +(-11.6190 + 6.70820i) q^{47} +(-38.0000 + 42.4853i) q^{48} +(-24.5000 - 42.4352i) q^{49} -44.7214i q^{50} +(16.4758 - 78.7943i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-17.4284 - 10.0623i) q^{53} +(60.1028 + 5.71414i) q^{54} +25.0000 q^{55} +(-40.6663 - 23.4787i) q^{56} +(32.0000 - 35.7771i) q^{57} +(-17.5000 - 30.3109i) q^{58} +(17.4284 + 10.0623i) q^{59} +(6.37298 - 2.09406i) q^{60} +(13.0000 + 22.5167i) q^{61} +6.70820i q^{62} +(7.00000 + 62.6099i) q^{63} -41.0000 q^{64} +(-3.87298 + 2.23607i) q^{65} +(-23.4123 - 71.2521i) q^{66} +(-26.0000 + 45.0333i) q^{67} +(-23.2379 + 13.4164i) q^{68} +(30.0000 + 26.8328i) q^{69} +(17.5000 + 30.3109i) q^{70} +93.9149i q^{71} +(35.8095 + 48.6074i) q^{72} +(-9.00000 + 15.5885i) q^{73} +(23.2379 + 13.4164i) q^{74} +(-58.7298 - 12.2803i) q^{75} -16.0000 q^{76} +(67.7772 - 39.1312i) q^{77} +(10.0000 + 8.94427i) q^{78} +(39.5000 + 68.4160i) q^{79} +(36.7933 + 21.2426i) q^{80} +(24.0081 - 77.3603i) q^{81} +(-35.0000 - 60.6218i) q^{82} -140.872i q^{83} +(14.0000 - 15.6525i) q^{84} -60.0000 q^{85} +(-85.2056 + 49.1935i) q^{86} +(-44.6109 + 14.6584i) q^{87} +(37.5000 - 64.9519i) q^{88} +(42.6028 - 24.5967i) q^{89} +(-5.00000 - 44.7214i) q^{90} +(-7.00000 + 12.1244i) q^{91} -13.4164i q^{92} +(8.80948 + 1.84205i) q^{93} +(15.0000 - 25.9808i) q^{94} +(-30.9839 - 17.8885i) q^{95} +(9.61088 - 45.9634i) q^{96} -93.0000 q^{97} +(94.8881 + 54.7837i) q^{98} +(-100.000 + 11.1803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 2 q^{4} - 20 q^{6} + 14 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 2 q^{4} - 20 q^{6} + 14 q^{7} + 2 q^{9} - 10 q^{10} + 4 q^{12} - 8 q^{13} + 20 q^{15} + 38 q^{16} + 40 q^{18} - 32 q^{19} + 28 q^{21} - 100 q^{22} + 30 q^{24} - 40 q^{25} - 88 q^{27} - 14 q^{28} - 20 q^{30} + 6 q^{31} + 50 q^{33} + 240 q^{34} + 4 q^{36} - 24 q^{37} + 8 q^{39} - 30 q^{40} - 70 q^{42} + 176 q^{43} - 40 q^{45} - 60 q^{46} - 152 q^{48} - 98 q^{49} - 120 q^{51} - 4 q^{52} + 70 q^{54} + 100 q^{55} + 128 q^{57} - 70 q^{58} + 10 q^{60} + 52 q^{61} + 28 q^{63} - 164 q^{64} + 100 q^{66} - 104 q^{67} + 120 q^{69} + 70 q^{70} + 120 q^{72} - 36 q^{73} - 80 q^{75} - 64 q^{76} + 40 q^{78} + 158 q^{79} + 158 q^{81} - 140 q^{82} + 56 q^{84} - 240 q^{85} - 70 q^{87} + 150 q^{88} - 20 q^{90} - 28 q^{91} + 12 q^{93} + 60 q^{94} - 70 q^{96} - 372 q^{97} - 400 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93649 + 1.11803i −0.968246 + 0.559017i −0.898701 0.438562i \(-0.855488\pi\)
−0.0695448 + 0.997579i \(0.522155\pi\)
\(3\) 0.936492 + 2.85008i 0.312164 + 0.950028i
\(4\) 0.500000 0.866025i 0.125000 0.216506i
\(5\) 1.93649 1.11803i 0.387298 0.223607i −0.293691 0.955901i \(-0.594884\pi\)
0.680989 + 0.732294i \(0.261550\pi\)
\(6\) −5.00000 4.47214i −0.833333 0.745356i
\(7\) 3.50000 6.06218i 0.500000 0.866025i
\(8\) 6.70820i 0.838525i
\(9\) −7.24597 + 5.33816i −0.805107 + 0.593129i
\(10\) −2.50000 + 4.33013i −0.250000 + 0.433013i
\(11\) 9.68246 + 5.59017i 0.880223 + 0.508197i 0.870732 0.491758i \(-0.163645\pi\)
0.00949140 + 0.999955i \(0.496979\pi\)
\(12\) 2.93649 + 0.614017i 0.244708 + 0.0511681i
\(13\) −2.00000 −0.153846 −0.0769231 0.997037i \(-0.524510\pi\)
−0.0769231 + 0.997037i \(0.524510\pi\)
\(14\) 15.6525i 1.11803i
\(15\) 5.00000 + 4.47214i 0.333333 + 0.298142i
\(16\) 9.50000 + 16.4545i 0.593750 + 1.02841i
\(17\) −23.2379 13.4164i −1.36694 0.789200i −0.376400 0.926457i \(-0.622838\pi\)
−0.990535 + 0.137257i \(0.956171\pi\)
\(18\) 8.06351 18.4385i 0.447973 1.02436i
\(19\) −8.00000 13.8564i −0.421053 0.729285i 0.574990 0.818160i \(-0.305006\pi\)
−0.996043 + 0.0888758i \(0.971673\pi\)
\(20\) 2.23607i 0.111803i
\(21\) 20.5554 + 4.29812i 0.978831 + 0.204672i
\(22\) −25.0000 −1.13636
\(23\) 11.6190 6.70820i 0.505172 0.291661i −0.225675 0.974203i \(-0.572459\pi\)
0.730847 + 0.682542i \(0.239125\pi\)
\(24\) 19.1190 6.28218i 0.796623 0.261757i
\(25\) −10.0000 + 17.3205i −0.400000 + 0.692820i
\(26\) 3.87298 2.23607i 0.148961 0.0860026i
\(27\) −22.0000 15.6525i −0.814815 0.579721i
\(28\) −3.50000 6.06218i −0.125000 0.216506i
\(29\) 15.6525i 0.539741i 0.962897 + 0.269870i \(0.0869808\pi\)
−0.962897 + 0.269870i \(0.913019\pi\)
\(30\) −14.6825 3.07008i −0.489415 0.102336i
\(31\) 1.50000 2.59808i 0.0483871 0.0838089i −0.840817 0.541319i \(-0.817925\pi\)
0.889205 + 0.457510i \(0.151259\pi\)
\(32\) −13.5554 7.82624i −0.423608 0.244570i
\(33\) −6.86492 + 32.8310i −0.208028 + 0.994878i
\(34\) 60.0000 1.76471
\(35\) 15.6525i 0.447214i
\(36\) 1.00000 + 8.94427i 0.0277778 + 0.248452i
\(37\) −6.00000 10.3923i −0.162162 0.280873i 0.773482 0.633819i \(-0.218513\pi\)
−0.935644 + 0.352946i \(0.885180\pi\)
\(38\) 30.9839 + 17.8885i 0.815365 + 0.470751i
\(39\) −1.87298 5.70017i −0.0480252 0.146158i
\(40\) −7.50000 12.9904i −0.187500 0.324760i
\(41\) 31.3050i 0.763535i 0.924258 + 0.381768i \(0.124685\pi\)
−0.924258 + 0.381768i \(0.875315\pi\)
\(42\) −44.6109 + 14.6584i −1.06216 + 0.349010i
\(43\) 44.0000 1.02326 0.511628 0.859207i \(-0.329043\pi\)
0.511628 + 0.859207i \(0.329043\pi\)
\(44\) 9.68246 5.59017i 0.220056 0.127049i
\(45\) −8.06351 + 18.4385i −0.179189 + 0.409745i
\(46\) −15.0000 + 25.9808i −0.326087 + 0.564799i
\(47\) −11.6190 + 6.70820i −0.247212 + 0.142728i −0.618487 0.785795i \(-0.712254\pi\)
0.371275 + 0.928523i \(0.378921\pi\)
\(48\) −38.0000 + 42.4853i −0.791667 + 0.885110i
\(49\) −24.5000 42.4352i −0.500000 0.866025i
\(50\) 44.7214i 0.894427i
\(51\) 16.4758 78.7943i 0.323055 1.54499i
\(52\) −1.00000 + 1.73205i −0.0192308 + 0.0333087i
\(53\) −17.4284 10.0623i −0.328838 0.189855i 0.326487 0.945202i \(-0.394135\pi\)
−0.655325 + 0.755347i \(0.727468\pi\)
\(54\) 60.1028 + 5.71414i 1.11302 + 0.105817i
\(55\) 25.0000 0.454545
\(56\) −40.6663 23.4787i −0.726184 0.419263i
\(57\) 32.0000 35.7771i 0.561404 0.627668i
\(58\) −17.5000 30.3109i −0.301724 0.522602i
\(59\) 17.4284 + 10.0623i 0.295397 + 0.170548i 0.640373 0.768064i \(-0.278780\pi\)
−0.344976 + 0.938611i \(0.612113\pi\)
\(60\) 6.37298 2.09406i 0.106216 0.0349010i
\(61\) 13.0000 + 22.5167i 0.213115 + 0.369126i 0.952688 0.303951i \(-0.0983058\pi\)
−0.739573 + 0.673076i \(0.764973\pi\)
\(62\) 6.70820i 0.108197i
\(63\) 7.00000 + 62.6099i 0.111111 + 0.993808i
\(64\) −41.0000 −0.640625
\(65\) −3.87298 + 2.23607i −0.0595844 + 0.0344010i
\(66\) −23.4123 71.2521i −0.354732 1.07958i
\(67\) −26.0000 + 45.0333i −0.388060 + 0.672139i −0.992189 0.124748i \(-0.960188\pi\)
0.604129 + 0.796887i \(0.293521\pi\)
\(68\) −23.2379 + 13.4164i −0.341734 + 0.197300i
\(69\) 30.0000 + 26.8328i 0.434783 + 0.388881i
\(70\) 17.5000 + 30.3109i 0.250000 + 0.433013i
\(71\) 93.9149i 1.32274i 0.750058 + 0.661372i \(0.230026\pi\)
−0.750058 + 0.661372i \(0.769974\pi\)
\(72\) 35.8095 + 48.6074i 0.497354 + 0.675103i
\(73\) −9.00000 + 15.5885i −0.123288 + 0.213541i −0.921062 0.389415i \(-0.872677\pi\)
0.797775 + 0.602956i \(0.206010\pi\)
\(74\) 23.2379 + 13.4164i 0.314026 + 0.181303i
\(75\) −58.7298 12.2803i −0.783064 0.163738i
\(76\) −16.0000 −0.210526
\(77\) 67.7772 39.1312i 0.880223 0.508197i
\(78\) 10.0000 + 8.94427i 0.128205 + 0.114670i
\(79\) 39.5000 + 68.4160i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 36.7933 + 21.2426i 0.459917 + 0.265533i
\(81\) 24.0081 77.3603i 0.296396 0.955065i
\(82\) −35.0000 60.6218i −0.426829 0.739290i
\(83\) 140.872i 1.69726i −0.528990 0.848628i \(-0.677429\pi\)
0.528990 0.848628i \(-0.322571\pi\)
\(84\) 14.0000 15.6525i 0.166667 0.186339i
\(85\) −60.0000 −0.705882
\(86\) −85.2056 + 49.1935i −0.990763 + 0.572017i
\(87\) −44.6109 + 14.6584i −0.512769 + 0.168488i
\(88\) 37.5000 64.9519i 0.426136 0.738090i
\(89\) 42.6028 24.5967i 0.478683 0.276368i −0.241184 0.970479i \(-0.577536\pi\)
0.719868 + 0.694111i \(0.244202\pi\)
\(90\) −5.00000 44.7214i −0.0555556 0.496904i
\(91\) −7.00000 + 12.1244i −0.0769231 + 0.133235i
\(92\) 13.4164i 0.145831i
\(93\) 8.80948 + 1.84205i 0.0947255 + 0.0198070i
\(94\) 15.0000 25.9808i 0.159574 0.276391i
\(95\) −30.9839 17.8885i −0.326146 0.188300i
\(96\) 9.61088 45.9634i 0.100113 0.478785i
\(97\) −93.0000 −0.958763 −0.479381 0.877607i \(-0.659139\pi\)
−0.479381 + 0.877607i \(0.659139\pi\)
\(98\) 94.8881 + 54.7837i 0.968246 + 0.559017i
\(99\) −100.000 + 11.1803i −1.01010 + 0.112933i
\(100\) 10.0000 + 17.3205i 0.100000 + 0.173205i
\(101\) −50.3488 29.0689i −0.498503 0.287811i 0.229592 0.973287i \(-0.426261\pi\)
−0.728095 + 0.685476i \(0.759594\pi\)
\(102\) 56.1895 + 171.005i 0.550877 + 1.67652i
\(103\) 41.0000 + 71.0141i 0.398058 + 0.689457i 0.993486 0.113952i \(-0.0363509\pi\)
−0.595428 + 0.803409i \(0.703018\pi\)
\(104\) 13.4164i 0.129004i
\(105\) 44.6109 14.6584i 0.424866 0.139604i
\(106\) 45.0000 0.424528
\(107\) −56.1583 + 32.4230i −0.524844 + 0.303019i −0.738914 0.673800i \(-0.764661\pi\)
0.214071 + 0.976818i \(0.431328\pi\)
\(108\) −24.5554 + 11.2263i −0.227365 + 0.103947i
\(109\) 72.0000 124.708i 0.660550 1.14411i −0.319921 0.947444i \(-0.603656\pi\)
0.980471 0.196663i \(-0.0630104\pi\)
\(110\) −48.4123 + 27.9508i −0.440112 + 0.254099i
\(111\) 24.0000 26.8328i 0.216216 0.241737i
\(112\) 133.000 1.18750
\(113\) 31.3050i 0.277035i −0.990360 0.138517i \(-0.955766\pi\)
0.990360 0.138517i \(-0.0442337\pi\)
\(114\) −21.9677 + 105.059i −0.192699 + 0.921571i
\(115\) 15.0000 25.9808i 0.130435 0.225920i
\(116\) 13.5554 + 7.82624i 0.116857 + 0.0674676i
\(117\) 14.4919 10.6763i 0.123863 0.0912506i
\(118\) −45.0000 −0.381356
\(119\) −162.665 + 93.9149i −1.36694 + 0.789200i
\(120\) 30.0000 33.5410i 0.250000 0.279508i
\(121\) 2.00000 + 3.46410i 0.0165289 + 0.0286289i
\(122\) −50.3488 29.0689i −0.412695 0.238270i
\(123\) −89.2218 + 29.3168i −0.725380 + 0.238348i
\(124\) −1.50000 2.59808i −0.0120968 0.0209522i
\(125\) 100.623i 0.804984i
\(126\) −83.5554 113.417i −0.663138 0.900137i
\(127\) 177.000 1.39370 0.696850 0.717217i \(-0.254584\pi\)
0.696850 + 0.717217i \(0.254584\pi\)
\(128\) 133.618 77.1443i 1.04389 0.602690i
\(129\) 41.2056 + 125.404i 0.319424 + 0.972122i
\(130\) 5.00000 8.66025i 0.0384615 0.0666173i
\(131\) 164.602 95.0329i 1.25650 0.725442i 0.284109 0.958792i \(-0.408302\pi\)
0.972393 + 0.233350i \(0.0749688\pi\)
\(132\) 25.0000 + 22.3607i 0.189394 + 0.169399i
\(133\) −112.000 −0.842105
\(134\) 116.276i 0.867728i
\(135\) −60.1028 5.71414i −0.445206 0.0423270i
\(136\) −90.0000 + 155.885i −0.661765 + 1.14621i
\(137\) 185.903 + 107.331i 1.35696 + 0.783440i 0.989213 0.146487i \(-0.0467966\pi\)
0.367745 + 0.929927i \(0.380130\pi\)
\(138\) −88.0948 18.4205i −0.638368 0.133482i
\(139\) −114.000 −0.820144 −0.410072 0.912053i \(-0.634496\pi\)
−0.410072 + 0.912053i \(0.634496\pi\)
\(140\) −13.5554 7.82624i −0.0968246 0.0559017i
\(141\) −30.0000 26.8328i −0.212766 0.190304i
\(142\) −105.000 181.865i −0.739437 1.28074i
\(143\) −19.3649 11.1803i −0.135419 0.0781842i
\(144\) −156.673 68.5161i −1.08801 0.475806i
\(145\) 17.5000 + 30.3109i 0.120690 + 0.209041i
\(146\) 40.2492i 0.275680i
\(147\) 98.0000 109.567i 0.666667 0.745356i
\(148\) −12.0000 −0.0810811
\(149\) 11.6190 6.70820i 0.0779795 0.0450215i −0.460503 0.887658i \(-0.652331\pi\)
0.538483 + 0.842637i \(0.318998\pi\)
\(150\) 127.460 41.8812i 0.849731 0.279208i
\(151\) −29.5000 + 51.0955i −0.195364 + 0.338381i −0.947020 0.321175i \(-0.895922\pi\)
0.751656 + 0.659556i \(0.229256\pi\)
\(152\) −92.9516 + 53.6656i −0.611524 + 0.353063i
\(153\) 240.000 26.8328i 1.56863 0.175378i
\(154\) −87.5000 + 151.554i −0.568182 + 0.984120i
\(155\) 6.70820i 0.0432787i
\(156\) −5.87298 1.22803i −0.0376473 0.00787201i
\(157\) 124.000 214.774i 0.789809 1.36799i −0.136275 0.990671i \(-0.543513\pi\)
0.926084 0.377318i \(-0.123154\pi\)
\(158\) −152.983 88.3247i −0.968246 0.559017i
\(159\) 12.3569 59.0958i 0.0777160 0.371671i
\(160\) −35.0000 −0.218750
\(161\) 93.9149i 0.583322i
\(162\) 40.0000 + 176.649i 0.246914 + 1.09043i
\(163\) 1.00000 + 1.73205i 0.00613497 + 0.0106261i 0.869077 0.494678i \(-0.164714\pi\)
−0.862942 + 0.505304i \(0.831380\pi\)
\(164\) 27.1109 + 15.6525i 0.165310 + 0.0954419i
\(165\) 23.4123 + 71.2521i 0.141893 + 0.431831i
\(166\) 157.500 + 272.798i 0.948795 + 1.64336i
\(167\) 250.440i 1.49964i 0.661643 + 0.749819i \(0.269860\pi\)
−0.661643 + 0.749819i \(0.730140\pi\)
\(168\) 28.8327 137.890i 0.171623 0.820774i
\(169\) −165.000 −0.976331
\(170\) 116.190 67.0820i 0.683468 0.394600i
\(171\) 131.935 + 57.6978i 0.771552 + 0.337414i
\(172\) 22.0000 38.1051i 0.127907 0.221541i
\(173\) −228.506 + 131.928i −1.32084 + 0.762590i −0.983863 0.178922i \(-0.942739\pi\)
−0.336981 + 0.941512i \(0.609406\pi\)
\(174\) 70.0000 78.2624i 0.402299 0.449784i
\(175\) 70.0000 + 121.244i 0.400000 + 0.692820i
\(176\) 212.426i 1.20697i
\(177\) −12.3569 + 59.0958i −0.0698127 + 0.333874i
\(178\) −55.0000 + 95.2628i −0.308989 + 0.535184i
\(179\) −166.538 96.1509i −0.930381 0.537156i −0.0434493 0.999056i \(-0.513835\pi\)
−0.886932 + 0.461900i \(0.847168\pi\)
\(180\) 11.9365 + 16.2025i 0.0663138 + 0.0900137i
\(181\) 82.0000 0.453039 0.226519 0.974007i \(-0.427265\pi\)
0.226519 + 0.974007i \(0.427265\pi\)
\(182\) 31.3050i 0.172005i
\(183\) −52.0000 + 58.1378i −0.284153 + 0.317693i
\(184\) −45.0000 77.9423i −0.244565 0.423599i
\(185\) −23.2379 13.4164i −0.125610 0.0725211i
\(186\) −19.1190 + 6.28218i −0.102790 + 0.0337751i
\(187\) −150.000 259.808i −0.802139 1.38935i
\(188\) 13.4164i 0.0713639i
\(189\) −171.888 + 78.5842i −0.909461 + 0.415790i
\(190\) 80.0000 0.421053
\(191\) 147.173 84.9706i 0.770541 0.444872i −0.0625264 0.998043i \(-0.519916\pi\)
0.833068 + 0.553171i \(0.186582\pi\)
\(192\) −38.3962 116.853i −0.199980 0.608612i
\(193\) −29.5000 + 51.0955i −0.152850 + 0.264744i −0.932274 0.361753i \(-0.882178\pi\)
0.779424 + 0.626496i \(0.215512\pi\)
\(194\) 180.094 103.977i 0.928318 0.535965i
\(195\) −10.0000 8.94427i −0.0512821 0.0458681i
\(196\) −49.0000 −0.250000
\(197\) 219.135i 1.11236i −0.831062 0.556179i \(-0.812267\pi\)
0.831062 0.556179i \(-0.187733\pi\)
\(198\) 181.149 133.454i 0.914895 0.674010i
\(199\) 117.000 202.650i 0.587940 1.01834i −0.406562 0.913623i \(-0.633273\pi\)
0.994502 0.104718i \(-0.0333941\pi\)
\(200\) 116.190 + 67.0820i 0.580948 + 0.335410i
\(201\) −152.698 31.9289i −0.759689 0.158850i
\(202\) 130.000 0.643564
\(203\) 94.8881 + 54.7837i 0.467429 + 0.269870i
\(204\) −60.0000 53.6656i −0.294118 0.263067i
\(205\) 35.0000 + 60.6218i 0.170732 + 0.295716i
\(206\) −158.792 91.6788i −0.770836 0.445043i
\(207\) −48.3810 + 110.631i −0.233725 + 0.534450i
\(208\) −19.0000 32.9090i −0.0913462 0.158216i
\(209\) 178.885i 0.855911i
\(210\) −70.0000 + 78.2624i −0.333333 + 0.372678i
\(211\) −26.0000 −0.123223 −0.0616114 0.998100i \(-0.519624\pi\)
−0.0616114 + 0.998100i \(0.519624\pi\)
\(212\) −17.4284 + 10.0623i −0.0822096 + 0.0474637i
\(213\) −267.665 + 87.9505i −1.25664 + 0.412913i
\(214\) 72.5000 125.574i 0.338785 0.586793i
\(215\) 85.2056 49.1935i 0.396305 0.228807i
\(216\) −105.000 + 147.580i −0.486111 + 0.683243i
\(217\) −10.5000 18.1865i −0.0483871 0.0838089i
\(218\) 321.994i 1.47704i
\(219\) −52.8569 11.0523i −0.241355 0.0504671i
\(220\) 12.5000 21.6506i 0.0568182 0.0984120i
\(221\) 46.4758 + 26.8328i 0.210298 + 0.121415i
\(222\) −16.4758 + 78.7943i −0.0742153 + 0.354929i
\(223\) −107.000 −0.479821 −0.239910 0.970795i \(-0.577118\pi\)
−0.239910 + 0.970795i \(0.577118\pi\)
\(224\) −94.8881 + 54.7837i −0.423608 + 0.244570i
\(225\) −20.0000 178.885i −0.0888889 0.795046i
\(226\) 35.0000 + 60.6218i 0.154867 + 0.268238i
\(227\) 261.426 + 150.935i 1.15166 + 0.664910i 0.949291 0.314400i \(-0.101803\pi\)
0.202367 + 0.979310i \(0.435137\pi\)
\(228\) −14.9839 45.6014i −0.0657187 0.200006i
\(229\) 167.000 + 289.252i 0.729258 + 1.26311i 0.957197 + 0.289436i \(0.0934678\pi\)
−0.227940 + 0.973675i \(0.573199\pi\)
\(230\) 67.0820i 0.291661i
\(231\) 175.000 + 156.525i 0.757576 + 0.677596i
\(232\) 105.000 0.452586
\(233\) −232.379 + 134.164i −0.997335 + 0.575811i −0.907459 0.420141i \(-0.861980\pi\)
−0.0898761 + 0.995953i \(0.528647\pi\)
\(234\) −16.1270 + 36.8771i −0.0689189 + 0.157594i
\(235\) −15.0000 + 25.9808i −0.0638298 + 0.110556i
\(236\) 17.4284 10.0623i 0.0738493 0.0426369i
\(237\) −158.000 + 176.649i −0.666667 + 0.745356i
\(238\) 210.000 363.731i 0.882353 1.52828i
\(239\) 281.745i 1.17885i −0.807824 0.589424i \(-0.799355\pi\)
0.807824 0.589424i \(-0.200645\pi\)
\(240\) −26.0867 + 124.758i −0.108695 + 0.519824i
\(241\) −89.5000 + 155.019i −0.371369 + 0.643230i −0.989776 0.142627i \(-0.954445\pi\)
0.618407 + 0.785858i \(0.287778\pi\)
\(242\) −7.74597 4.47214i −0.0320081 0.0184799i
\(243\) 242.967 4.02223i 0.999863 0.0165524i
\(244\) 26.0000 0.106557
\(245\) −94.8881 54.7837i −0.387298 0.223607i
\(246\) 140.000 156.525i 0.569106 0.636280i
\(247\) 16.0000 + 27.7128i 0.0647773 + 0.112198i
\(248\) −17.4284 10.0623i −0.0702759 0.0405738i
\(249\) 401.498 131.926i 1.61244 0.529822i
\(250\) −112.500 194.856i −0.450000 0.779423i
\(251\) 172.177i 0.685965i −0.939342 0.342983i \(-0.888563\pi\)
0.939342 0.342983i \(-0.111437\pi\)
\(252\) 57.7218 + 25.2428i 0.229055 + 0.100170i
\(253\) 150.000 0.592885
\(254\) −342.759 + 197.892i −1.34944 + 0.779102i
\(255\) −56.1895 171.005i −0.220351 0.670608i
\(256\) −90.5000 + 156.751i −0.353516 + 0.612307i
\(257\) −228.506 + 131.928i −0.889128 + 0.513339i −0.873657 0.486542i \(-0.838258\pi\)
−0.0154711 + 0.999880i \(0.504925\pi\)
\(258\) −220.000 196.774i −0.852713 0.762690i
\(259\) −84.0000 −0.324324
\(260\) 4.47214i 0.0172005i
\(261\) −83.5554 113.417i −0.320136 0.434549i
\(262\) −212.500 + 368.061i −0.811069 + 1.40481i
\(263\) −30.9839 17.8885i −0.117809 0.0680173i 0.439937 0.898028i \(-0.355001\pi\)
−0.557747 + 0.830011i \(0.688334\pi\)
\(264\) 220.237 + 46.0513i 0.834231 + 0.174437i
\(265\) −45.0000 −0.169811
\(266\) 216.887 125.220i 0.815365 0.470751i
\(267\) 110.000 + 98.3870i 0.411985 + 0.368491i
\(268\) 26.0000 + 45.0333i 0.0970149 + 0.168035i
\(269\) 342.759 + 197.892i 1.27420 + 0.735658i 0.975775 0.218776i \(-0.0702064\pi\)
0.298422 + 0.954434i \(0.403540\pi\)
\(270\) 122.777 56.1316i 0.454730 0.207895i
\(271\) −228.500 395.774i −0.843173 1.46042i −0.887198 0.461389i \(-0.847351\pi\)
0.0440246 0.999030i \(-0.485982\pi\)
\(272\) 509.823i 1.87435i
\(273\) −41.1109 8.59624i −0.150589 0.0314880i
\(274\) −480.000 −1.75182
\(275\) −193.649 + 111.803i −0.704179 + 0.406558i
\(276\) 38.2379 12.5644i 0.138543 0.0455230i
\(277\) −26.0000 + 45.0333i −0.0938628 + 0.162575i −0.909133 0.416505i \(-0.863255\pi\)
0.815271 + 0.579080i \(0.196588\pi\)
\(278\) 220.760 127.456i 0.794101 0.458474i
\(279\) 3.00000 + 26.8328i 0.0107527 + 0.0961750i
\(280\) −105.000 −0.375000
\(281\) 125.220i 0.445622i 0.974862 + 0.222811i \(0.0715233\pi\)
−0.974862 + 0.222811i \(0.928477\pi\)
\(282\) 88.0948 + 18.4205i 0.312393 + 0.0653209i
\(283\) −44.0000 + 76.2102i −0.155477 + 0.269294i −0.933233 0.359273i \(-0.883025\pi\)
0.777756 + 0.628567i \(0.216358\pi\)
\(284\) 81.3327 + 46.9574i 0.286383 + 0.165343i
\(285\) 21.9677 105.059i 0.0770798 0.368628i
\(286\) 50.0000 0.174825
\(287\) 189.776 + 109.567i 0.661241 + 0.381768i
\(288\) 140.000 15.6525i 0.486111 0.0543489i
\(289\) 215.500 + 373.257i 0.745675 + 1.29155i
\(290\) −67.7772 39.1312i −0.233715 0.134935i
\(291\) −87.0937 265.058i −0.299291 0.910852i
\(292\) 9.00000 + 15.5885i 0.0308219 + 0.0533851i
\(293\) 15.6525i 0.0534214i −0.999643 0.0267107i \(-0.991497\pi\)
0.999643 0.0267107i \(-0.00850329\pi\)
\(294\) −67.2762 + 321.744i −0.228831 + 1.09437i
\(295\) 45.0000 0.152542
\(296\) −69.7137 + 40.2492i −0.235519 + 0.135977i
\(297\) −125.514 274.538i −0.422606 0.924371i
\(298\) −15.0000 + 25.9808i −0.0503356 + 0.0871838i
\(299\) −23.2379 + 13.4164i −0.0777187 + 0.0448709i
\(300\) −40.0000 + 44.7214i −0.133333 + 0.149071i
\(301\) 154.000 266.736i 0.511628 0.886166i
\(302\) 131.928i 0.436848i
\(303\) 35.6976 170.721i 0.117814 0.563436i
\(304\) 152.000 263.272i 0.500000 0.866025i
\(305\) 50.3488 + 29.0689i 0.165078 + 0.0953078i
\(306\) −434.758 + 320.290i −1.42078 + 1.04670i
\(307\) 166.000 0.540717 0.270358 0.962760i \(-0.412858\pi\)
0.270358 + 0.962760i \(0.412858\pi\)
\(308\) 78.2624i 0.254099i
\(309\) −164.000 + 183.358i −0.530744 + 0.593390i
\(310\) 7.50000 + 12.9904i 0.0241935 + 0.0419045i
\(311\) −267.236 154.289i −0.859279 0.496105i 0.00449160 0.999990i \(-0.498570\pi\)
−0.863771 + 0.503885i \(0.831904\pi\)
\(312\) −38.2379 + 12.5644i −0.122557 + 0.0402704i
\(313\) 135.500 + 234.693i 0.432907 + 0.749818i 0.997122 0.0758104i \(-0.0241544\pi\)
−0.564215 + 0.825628i \(0.690821\pi\)
\(314\) 554.545i 1.76607i
\(315\) 83.5554 + 113.417i 0.265255 + 0.360055i
\(316\) 79.0000 0.250000
\(317\) 377.616 218.017i 1.19122 0.687750i 0.232635 0.972564i \(-0.425265\pi\)
0.958583 + 0.284815i \(0.0919320\pi\)
\(318\) 42.1421 + 128.254i 0.132522 + 0.403314i
\(319\) −87.5000 + 151.554i −0.274295 + 0.475092i
\(320\) −79.3962 + 45.8394i −0.248113 + 0.143248i
\(321\) −145.000 129.692i −0.451713 0.404025i
\(322\) 105.000 + 181.865i 0.326087 + 0.564799i
\(323\) 429.325i 1.32918i
\(324\) −54.9919 59.4717i −0.169728 0.183555i
\(325\) 20.0000 34.6410i 0.0615385 0.106588i
\(326\) −3.87298 2.23607i −0.0118803 0.00685910i
\(327\) 422.855 + 88.4184i 1.29313 + 0.270393i
\(328\) 210.000 0.640244
\(329\) 93.9149i 0.285455i
\(330\) −125.000 111.803i −0.378788 0.338798i
\(331\) 8.00000 + 13.8564i 0.0241692 + 0.0418623i 0.877857 0.478923i \(-0.158973\pi\)
−0.853688 + 0.520785i \(0.825639\pi\)
\(332\) −121.999 70.4361i −0.367467 0.212157i
\(333\) 98.9516 + 43.2733i 0.297152 + 0.129950i
\(334\) −280.000 484.974i −0.838323 1.45202i
\(335\) 116.276i 0.347091i
\(336\) 124.553 + 379.061i 0.370695 + 1.12816i
\(337\) −509.000 −1.51039 −0.755193 0.655503i \(-0.772457\pi\)
−0.755193 + 0.655503i \(0.772457\pi\)
\(338\) 319.521 184.476i 0.945329 0.545786i
\(339\) 89.2218 29.3168i 0.263191 0.0864803i
\(340\) −30.0000 + 51.9615i −0.0882353 + 0.152828i
\(341\) 29.0474 16.7705i 0.0851829 0.0491804i
\(342\) −320.000 + 35.7771i −0.935673 + 0.104611i
\(343\) −343.000 −1.00000
\(344\) 295.161i 0.858026i
\(345\) 88.0948 + 18.4205i 0.255347 + 0.0533928i
\(346\) 295.000 510.955i 0.852601 1.47675i
\(347\) −329.204 190.066i −0.948713 0.547740i −0.0560324 0.998429i \(-0.517845\pi\)
−0.892681 + 0.450689i \(0.851178\pi\)
\(348\) −9.61088 + 45.9634i −0.0276175 + 0.132079i
\(349\) 628.000 1.79943 0.899713 0.436481i \(-0.143775\pi\)
0.899713 + 0.436481i \(0.143775\pi\)
\(350\) −271.109 156.525i −0.774597 0.447214i
\(351\) 44.0000 + 31.3050i 0.125356 + 0.0891879i
\(352\) −87.5000 151.554i −0.248580 0.430552i
\(353\) −402.790 232.551i −1.14105 0.658785i −0.194359 0.980931i \(-0.562263\pi\)
−0.946690 + 0.322146i \(0.895596\pi\)
\(354\) −42.1421 128.254i −0.119046 0.362299i
\(355\) 105.000 + 181.865i 0.295775 + 0.512297i
\(356\) 49.1935i 0.138184i
\(357\) −420.000 375.659i −1.17647 1.05227i
\(358\) 430.000 1.20112
\(359\) 201.395 116.276i 0.560989 0.323887i −0.192553 0.981287i \(-0.561677\pi\)
0.753542 + 0.657399i \(0.228343\pi\)
\(360\) 123.690 + 54.0917i 0.343582 + 0.150255i
\(361\) 52.5000 90.9327i 0.145429 0.251891i
\(362\) −158.792 + 91.6788i −0.438653 + 0.253256i
\(363\) −8.00000 + 8.94427i −0.0220386 + 0.0246399i
\(364\) 7.00000 + 12.1244i 0.0192308 + 0.0333087i
\(365\) 40.2492i 0.110272i
\(366\) 35.6976 170.721i 0.0975343 0.466451i
\(367\) −250.500 + 433.879i −0.682561 + 1.18223i 0.291635 + 0.956530i \(0.405801\pi\)
−0.974197 + 0.225701i \(0.927533\pi\)
\(368\) 220.760 + 127.456i 0.599891 + 0.346347i
\(369\) −167.111 226.835i −0.452875 0.614728i
\(370\) 60.0000 0.162162
\(371\) −121.999 + 70.4361i −0.328838 + 0.189855i
\(372\) 6.00000 6.70820i 0.0161290 0.0180328i
\(373\) −349.000 604.486i −0.935657 1.62061i −0.773458 0.633847i \(-0.781475\pi\)
−0.162198 0.986758i \(-0.551858\pi\)
\(374\) 580.948 + 335.410i 1.55334 + 0.896819i
\(375\) −286.784 + 94.2327i −0.764758 + 0.251287i
\(376\) 45.0000 + 77.9423i 0.119681 + 0.207293i
\(377\) 31.3050i 0.0830370i
\(378\) 245.000 344.354i 0.648148 0.910991i
\(379\) 366.000 0.965699 0.482850 0.875703i \(-0.339602\pi\)
0.482850 + 0.875703i \(0.339602\pi\)
\(380\) −30.9839 + 17.8885i −0.0815365 + 0.0470751i
\(381\) 165.759 + 504.465i 0.435063 + 1.32406i
\(382\) −190.000 + 329.090i −0.497382 + 0.861491i
\(383\) −11.6190 + 6.70820i −0.0303367 + 0.0175149i −0.515092 0.857135i \(-0.672242\pi\)
0.484755 + 0.874650i \(0.338909\pi\)
\(384\) 345.000 + 308.577i 0.898438 + 0.803587i
\(385\) 87.5000 151.554i 0.227273 0.393648i
\(386\) 131.928i 0.341782i
\(387\) −318.823 + 234.879i −0.823831 + 0.606923i
\(388\) −46.5000 + 80.5404i −0.119845 + 0.207578i
\(389\) −58.0948 33.5410i −0.149344 0.0862237i 0.423466 0.905912i \(-0.360813\pi\)
−0.572810 + 0.819688i \(0.694147\pi\)
\(390\) 29.3649 + 6.14017i 0.0752947 + 0.0157440i
\(391\) −360.000 −0.920716
\(392\) −284.664 + 164.351i −0.726184 + 0.419263i
\(393\) 425.000 + 380.132i 1.08142 + 0.967256i
\(394\) 245.000 + 424.352i 0.621827 + 1.07704i
\(395\) 152.983 + 88.3247i 0.387298 + 0.223607i
\(396\) −40.3175 + 92.1927i −0.101812 + 0.232810i
\(397\) 132.000 + 228.631i 0.332494 + 0.575896i 0.983000 0.183605i \(-0.0587766\pi\)
−0.650506 + 0.759501i \(0.725443\pi\)
\(398\) 523.240i 1.31467i
\(399\) −104.887 319.209i −0.262875 0.800024i
\(400\) −380.000 −0.950000
\(401\) 92.9516 53.6656i 0.231800 0.133830i −0.379602 0.925150i \(-0.623939\pi\)
0.611402 + 0.791320i \(0.290606\pi\)
\(402\) 331.395 108.891i 0.824366 0.270873i
\(403\) −3.00000 + 5.19615i −0.00744417 + 0.0128937i
\(404\) −50.3488 + 29.0689i −0.124626 + 0.0719527i
\(405\) −40.0000 176.649i −0.0987654 0.436171i
\(406\) −245.000 −0.603448
\(407\) 134.164i 0.329641i
\(408\) −528.569 110.523i −1.29551 0.270890i
\(409\) 99.5000 172.339i 0.243276 0.421367i −0.718369 0.695662i \(-0.755111\pi\)
0.961646 + 0.274295i \(0.0884445\pi\)
\(410\) −135.554 78.2624i −0.330621 0.190884i
\(411\) −131.806 + 630.355i −0.320697 + 1.53371i
\(412\) 82.0000 0.199029
\(413\) 121.999 70.4361i 0.295397 0.170548i
\(414\) −30.0000 268.328i −0.0724638 0.648136i
\(415\) −157.500 272.798i −0.379518 0.657345i
\(416\) 27.1109 + 15.6525i 0.0651704 + 0.0376261i
\(417\) −106.760 324.910i −0.256019 0.779160i
\(418\) 200.000 + 346.410i 0.478469 + 0.828732i
\(419\) 93.9149i 0.224140i −0.993700 0.112070i \(-0.964252\pi\)
0.993700 0.112070i \(-0.0357482\pi\)
\(420\) 9.61088 45.9634i 0.0228831 0.109437i
\(421\) 254.000 0.603325 0.301663 0.953415i \(-0.402458\pi\)
0.301663 + 0.953415i \(0.402458\pi\)
\(422\) 50.3488 29.0689i 0.119310 0.0688836i
\(423\) 48.3810 110.631i 0.114376 0.261540i
\(424\) −67.5000 + 116.913i −0.159198 + 0.275739i
\(425\) 464.758 268.328i 1.09355 0.631360i
\(426\) 420.000 469.574i 0.985915 1.10229i
\(427\) 182.000 0.426230
\(428\) 64.8460i 0.151509i
\(429\) 13.7298 65.6619i 0.0320043 0.153058i
\(430\) −110.000 + 190.526i −0.255814 + 0.443083i
\(431\) 104.571 + 60.3738i 0.242623 + 0.140079i 0.616382 0.787447i \(-0.288598\pi\)
−0.373759 + 0.927526i \(0.621931\pi\)
\(432\) 48.5534 510.697i 0.112392 1.18217i
\(433\) −506.000 −1.16859 −0.584296 0.811541i \(-0.698629\pi\)
−0.584296 + 0.811541i \(0.698629\pi\)
\(434\) 40.6663 + 23.4787i 0.0937012 + 0.0540984i
\(435\) −70.0000 + 78.2624i −0.160920 + 0.179914i
\(436\) −72.0000 124.708i −0.165138 0.286027i
\(437\) −185.903 107.331i −0.425408 0.245609i
\(438\) 114.714 37.6931i 0.261903 0.0860572i
\(439\) −235.500 407.898i −0.536446 0.929153i −0.999092 0.0426091i \(-0.986433\pi\)
0.462645 0.886543i \(-0.346900\pi\)
\(440\) 167.705i 0.381148i
\(441\) 404.052 + 176.699i 0.916219 + 0.400679i
\(442\) −120.000 −0.271493
\(443\) 52.2853 30.1869i 0.118025 0.0681420i −0.439825 0.898083i \(-0.644960\pi\)
0.557851 + 0.829941i \(0.311626\pi\)
\(444\) −11.2379 34.2010i −0.0253106 0.0770293i
\(445\) 55.0000 95.2628i 0.123596 0.214074i
\(446\) 207.205 119.630i 0.464584 0.268228i
\(447\) 30.0000 + 26.8328i 0.0671141 + 0.0600287i
\(448\) −143.500 + 248.549i −0.320312 + 0.554798i
\(449\) 281.745i 0.627493i −0.949507 0.313747i \(-0.898416\pi\)
0.949507 0.313747i \(-0.101584\pi\)
\(450\) 238.730 + 324.049i 0.530511 + 0.720110i
\(451\) −175.000 + 303.109i −0.388027 + 0.672082i
\(452\) −27.1109 15.6525i −0.0599798 0.0346294i
\(453\) −173.253 36.2270i −0.382457 0.0799713i
\(454\) −675.000 −1.48678
\(455\) 31.3050i 0.0688021i
\(456\) −240.000 214.663i −0.526316 0.470751i
\(457\) 11.5000 + 19.9186i 0.0251641 + 0.0435855i 0.878333 0.478049i \(-0.158656\pi\)
−0.853169 + 0.521634i \(0.825323\pi\)
\(458\) −646.788 373.423i −1.41220 0.815335i
\(459\) 301.234 + 658.892i 0.656283 + 1.43549i
\(460\) −15.0000 25.9808i −0.0326087 0.0564799i
\(461\) 594.794i 1.29023i 0.764087 + 0.645113i \(0.223190\pi\)
−0.764087 + 0.645113i \(0.776810\pi\)
\(462\) −513.886 107.453i −1.11231 0.232582i
\(463\) 58.0000 0.125270 0.0626350 0.998037i \(-0.480050\pi\)
0.0626350 + 0.998037i \(0.480050\pi\)
\(464\) −257.553 + 148.699i −0.555072 + 0.320471i
\(465\) 19.1190 6.28218i 0.0411160 0.0135101i
\(466\) 300.000 519.615i 0.643777 1.11505i
\(467\) −499.615 + 288.453i −1.06984 + 0.617672i −0.928137 0.372238i \(-0.878591\pi\)
−0.141702 + 0.989909i \(0.545257\pi\)
\(468\) −2.00000 17.8885i −0.00427350 0.0382234i
\(469\) 182.000 + 315.233i 0.388060 + 0.672139i
\(470\) 67.0820i 0.142728i
\(471\) 728.250 + 152.276i 1.54618 + 0.323304i
\(472\) 67.5000 116.913i 0.143008 0.247698i
\(473\) 426.028 + 245.967i 0.900694 + 0.520016i
\(474\) 108.466 518.729i 0.228831 1.09437i
\(475\) 320.000 0.673684
\(476\) 187.830i 0.394600i
\(477\) 180.000 20.1246i 0.377358 0.0421900i
\(478\) 315.000 + 545.596i 0.658996 + 1.14141i
\(479\) −294.347 169.941i −0.614503 0.354783i 0.160223 0.987081i \(-0.448779\pi\)
−0.774726 + 0.632298i \(0.782112\pi\)
\(480\) −32.7772 99.7530i −0.0682859 0.207819i
\(481\) 12.0000 + 20.7846i 0.0249480 + 0.0432112i
\(482\) 400.256i 0.830407i
\(483\) 267.665 87.9505i 0.554172 0.182092i
\(484\) 4.00000 0.00826446
\(485\) −180.094 + 103.977i −0.371327 + 0.214386i
\(486\) −466.006 + 279.434i −0.958860 + 0.574967i
\(487\) 404.500 700.615i 0.830595 1.43863i −0.0669712 0.997755i \(-0.521334\pi\)
0.897567 0.440879i \(-0.145333\pi\)
\(488\) 151.046 87.2067i 0.309521 0.178702i
\(489\) −4.00000 + 4.47214i −0.00817996 + 0.00914547i
\(490\) 245.000 0.500000
\(491\) 453.922i 0.924484i 0.886754 + 0.462242i \(0.152955\pi\)
−0.886754 + 0.462242i \(0.847045\pi\)
\(492\) −19.2218 + 91.9267i −0.0390686 + 0.186843i
\(493\) 210.000 363.731i 0.425963 0.737790i
\(494\) −61.9677 35.7771i −0.125441 0.0724233i
\(495\) −181.149 + 133.454i −0.365958 + 0.269604i
\(496\) 57.0000 0.114919
\(497\) 569.329 + 328.702i 1.14553 + 0.661372i
\(498\) −630.000 + 704.361i −1.26506 + 1.41438i
\(499\) 127.000 + 219.970i 0.254509 + 0.440823i 0.964762 0.263124i \(-0.0847528\pi\)
−0.710253 + 0.703946i \(0.751419\pi\)
\(500\) 87.1421 + 50.3115i 0.174284 + 0.100623i
\(501\) −713.774 + 234.535i −1.42470 + 0.468133i
\(502\) 192.500 + 333.420i 0.383466 + 0.664183i
\(503\) 939.149i 1.86709i −0.358454 0.933547i \(-0.616696\pi\)
0.358454 0.933547i \(-0.383304\pi\)
\(504\) 420.000 46.9574i 0.833333 0.0931695i
\(505\) −130.000 −0.257426
\(506\) −290.474 + 167.705i −0.574059 + 0.331433i
\(507\) −154.521 470.264i −0.304775 0.927542i
\(508\) 88.5000 153.286i 0.174213 0.301745i
\(509\) −350.505 + 202.364i −0.688615 + 0.397572i −0.803093 0.595854i \(-0.796814\pi\)
0.114478 + 0.993426i \(0.463480\pi\)
\(510\) 300.000 + 268.328i 0.588235 + 0.526134i
\(511\) 63.0000 + 109.119i 0.123288 + 0.213541i
\(512\) 212.426i 0.414895i
\(513\) −40.8871 + 430.061i −0.0797019 + 0.838325i
\(514\) 295.000 510.955i 0.573930 0.994076i
\(515\) 158.792 + 91.6788i 0.308335 + 0.178017i
\(516\) 129.206 + 27.0167i 0.250399 + 0.0523580i
\(517\) −150.000 −0.290135
\(518\) 162.665 93.9149i 0.314026 0.181303i
\(519\) −590.000 527.712i −1.13680 1.01679i
\(520\) 15.0000 + 25.9808i 0.0288462 + 0.0499630i
\(521\) 302.093 + 174.413i 0.579832 + 0.334766i 0.761067 0.648674i \(-0.224676\pi\)
−0.181234 + 0.983440i \(0.558009\pi\)
\(522\) 288.609 + 126.214i 0.552890 + 0.241789i
\(523\) −197.000 341.214i −0.376673 0.652417i 0.613903 0.789382i \(-0.289599\pi\)
−0.990576 + 0.136965i \(0.956265\pi\)
\(524\) 190.066i 0.362721i
\(525\) −280.000 + 313.050i −0.533333 + 0.596285i
\(526\) 80.0000 0.152091
\(527\) −69.7137 + 40.2492i −0.132284 + 0.0763742i
\(528\) −605.433 + 198.936i −1.14665 + 0.376772i
\(529\) −174.500 + 302.243i −0.329868 + 0.571348i
\(530\) 87.1421 50.3115i 0.164419 0.0949274i
\(531\) −180.000 + 20.1246i −0.338983 + 0.0378995i
\(532\) −56.0000 + 96.9948i −0.105263 + 0.182321i
\(533\) 62.6099i 0.117467i
\(534\) −323.014 67.5419i −0.604895 0.126483i
\(535\) −72.5000 + 125.574i −0.135514 + 0.234717i
\(536\) 302.093 + 174.413i 0.563606 + 0.325398i
\(537\) 118.077 564.693i 0.219882 1.05157i
\(538\) −885.000 −1.64498
\(539\) 547.837i 1.01639i
\(540\) −35.0000 + 49.1935i −0.0648148 + 0.0910991i
\(541\) −202.000 349.874i −0.373383 0.646718i 0.616701 0.787198i \(-0.288469\pi\)
−0.990084 + 0.140480i \(0.955135\pi\)
\(542\) 884.977 + 510.942i 1.63280 + 0.942697i
\(543\) 76.7923 + 233.707i 0.141422 + 0.430400i
\(544\) 210.000 + 363.731i 0.386029 + 0.668623i
\(545\) 321.994i 0.590814i
\(546\) 89.2218 29.3168i 0.163410 0.0536938i
\(547\) 16.0000 0.0292505 0.0146252 0.999893i \(-0.495344\pi\)
0.0146252 + 0.999893i \(0.495344\pi\)
\(548\) 185.903 107.331i 0.339239 0.195860i
\(549\) −214.395 93.7589i −0.390519 0.170781i
\(550\) 250.000 433.013i 0.454545 0.787296i
\(551\) 216.887 125.220i 0.393624 0.227259i
\(552\) 180.000 201.246i 0.326087 0.364576i
\(553\) 553.000 1.00000
\(554\) 116.276i 0.209884i
\(555\) 16.4758 78.7943i 0.0296861 0.141972i
\(556\) −57.0000 + 98.7269i −0.102518 + 0.177566i
\(557\) −640.979 370.069i −1.15077 0.664397i −0.201695 0.979448i \(-0.564645\pi\)
−0.949075 + 0.315051i \(0.897978\pi\)
\(558\) −35.8095 48.6074i −0.0641747 0.0871101i
\(559\) −88.0000 −0.157424
\(560\) 257.553 148.699i 0.459917 0.265533i
\(561\) 600.000 670.820i 1.06952 1.19576i
\(562\) −140.000 242.487i −0.249110 0.431472i
\(563\) 207.205 + 119.630i 0.368037 + 0.212486i 0.672600 0.740006i \(-0.265177\pi\)
−0.304564 + 0.952492i \(0.598511\pi\)
\(564\) −38.2379 + 12.5644i −0.0677977 + 0.0222772i
\(565\) −35.0000 60.6218i −0.0619469 0.107295i
\(566\) 196.774i 0.347657i
\(567\) −384.944 416.302i −0.678913 0.734219i
\(568\) 630.000 1.10915
\(569\) −828.818 + 478.519i −1.45662 + 0.840982i −0.998843 0.0480841i \(-0.984688\pi\)
−0.457780 + 0.889066i \(0.651355\pi\)
\(570\) 74.9193 + 228.007i 0.131437 + 0.400012i
\(571\) 23.0000 39.8372i 0.0402802 0.0697674i −0.845182 0.534478i \(-0.820508\pi\)
0.885463 + 0.464711i \(0.153842\pi\)
\(572\) −19.3649 + 11.1803i −0.0338547 + 0.0195460i
\(573\) 380.000 + 339.882i 0.663176 + 0.593163i
\(574\) −490.000 −0.853659
\(575\) 268.328i 0.466658i
\(576\) 297.085 218.865i 0.515772 0.379973i
\(577\) −495.500 + 858.231i −0.858752 + 1.48740i 0.0143677 + 0.999897i \(0.495426\pi\)
−0.873120 + 0.487506i \(0.837907\pi\)
\(578\) −834.628 481.873i −1.44399 0.833690i
\(579\) −173.253 36.2270i −0.299228 0.0625682i
\(580\) 35.0000 0.0603448
\(581\) −853.993 493.053i −1.46987 0.848628i
\(582\) 465.000 + 415.909i 0.798969 + 0.714620i
\(583\) −112.500 194.856i −0.192967 0.334229i
\(584\) 104.571 + 60.3738i 0.179059 + 0.103380i
\(585\) 16.1270 36.8771i 0.0275675 0.0630378i
\(586\) 17.5000 + 30.3109i 0.0298635 + 0.0517251i
\(587\) 766.971i 1.30660i 0.757101 + 0.653298i \(0.226615\pi\)
−0.757101 + 0.653298i \(0.773385\pi\)
\(588\) −45.8881 139.654i −0.0780410 0.237507i
\(589\) −48.0000 −0.0814941
\(590\) −87.1421 + 50.3115i −0.147699 + 0.0852738i
\(591\) 624.552 205.218i 1.05677 0.347238i
\(592\) 114.000 197.454i 0.192568 0.333537i
\(593\) 151.046 87.2067i 0.254716 0.147060i −0.367206 0.930140i \(-0.619686\pi\)
0.621922 + 0.783080i \(0.286352\pi\)
\(594\) 550.000 + 391.312i 0.925926 + 0.658774i
\(595\) −210.000 + 363.731i −0.352941 + 0.611312i
\(596\) 13.4164i 0.0225108i
\(597\) 687.139 + 143.680i 1.15099 + 0.240670i
\(598\) 30.0000 51.9615i 0.0501672 0.0868922i
\(599\) 836.564 + 482.991i 1.39660 + 0.806328i 0.994035 0.109062i \(-0.0347848\pi\)
0.402567 + 0.915391i \(0.368118\pi\)
\(600\) −82.3790 + 393.972i −0.137298 + 0.656619i
\(601\) −471.000 −0.783694 −0.391847 0.920030i \(-0.628164\pi\)
−0.391847 + 0.920030i \(0.628164\pi\)
\(602\) 688.709i 1.14403i
\(603\) −52.0000 465.102i −0.0862355 0.771314i
\(604\) 29.5000 + 51.0955i 0.0488411 + 0.0845952i
\(605\) 7.74597 + 4.47214i 0.0128033 + 0.00739196i
\(606\) 121.744 + 370.511i 0.200898 + 0.611404i
\(607\) 471.500 + 816.662i 0.776771 + 1.34541i 0.933794 + 0.357812i \(0.116477\pi\)
−0.157023 + 0.987595i \(0.550190\pi\)
\(608\) 250.440i 0.411907i
\(609\) −67.2762 + 321.744i −0.110470 + 0.528315i
\(610\) −130.000 −0.213115
\(611\) 23.2379 13.4164i 0.0380326 0.0219581i
\(612\) 96.7621 221.263i 0.158108 0.361540i
\(613\) −467.000 + 808.868i −0.761827 + 1.31952i 0.180081 + 0.983652i \(0.442364\pi\)
−0.941908 + 0.335871i \(0.890969\pi\)
\(614\) −321.458 + 185.594i −0.523547 + 0.302270i
\(615\) −140.000 + 156.525i −0.227642 + 0.254512i
\(616\) −262.500 454.663i −0.426136 0.738090i
\(617\) 93.9149i 0.152212i 0.997100 + 0.0761060i \(0.0242488\pi\)
−0.997100 + 0.0761060i \(0.975751\pi\)
\(618\) 112.585 538.428i 0.182176 0.871243i
\(619\) 61.0000 105.655i 0.0985460 0.170687i −0.812537 0.582910i \(-0.801914\pi\)
0.911083 + 0.412223i \(0.135247\pi\)
\(620\) −5.80948 3.35410i −0.00937012 0.00540984i
\(621\) −360.617 34.2848i −0.580704 0.0552091i
\(622\) 690.000 1.10932
\(623\) 344.354i 0.552736i
\(624\) 76.0000 84.9706i 0.121795 0.136171i
\(625\) −137.500 238.157i −0.220000 0.381051i
\(626\) −524.789 302.987i −0.838321 0.484005i
\(627\) 509.839 167.525i 0.813140 0.267185i
\(628\) −124.000 214.774i −0.197452 0.341997i
\(629\) 321.994i 0.511914i
\(630\) −288.609 126.214i −0.458109 0.200339i
\(631\) −61.0000 −0.0966719 −0.0483360 0.998831i \(-0.515392\pi\)
−0.0483360 + 0.998831i \(0.515392\pi\)
\(632\) 458.949 264.974i 0.726184 0.419263i
\(633\) −24.3488 74.1022i −0.0384657 0.117065i
\(634\) −487.500 + 844.375i −0.768927 + 1.33182i
\(635\) 342.759 197.892i 0.539778 0.311641i
\(636\) −45.0000 40.2492i −0.0707547 0.0632849i
\(637\) 49.0000 + 84.8705i 0.0769231 + 0.133235i
\(638\) 391.312i 0.613342i
\(639\) −501.333 680.504i −0.784558 1.06495i
\(640\) 172.500 298.779i 0.269531 0.466842i
\(641\) −708.756 409.200i −1.10570 0.638378i −0.167990 0.985789i \(-0.553728\pi\)
−0.937713 + 0.347410i \(0.887061\pi\)
\(642\) 425.791 + 89.0324i 0.663226 + 0.138680i
\(643\) 908.000 1.41213 0.706065 0.708147i \(-0.250468\pi\)
0.706065 + 0.708147i \(0.250468\pi\)
\(644\) −81.3327 46.9574i −0.126293 0.0729153i
\(645\) 220.000 + 196.774i 0.341085 + 0.305076i
\(646\) −480.000 831.384i −0.743034 1.28697i
\(647\) 274.982 + 158.761i 0.425011 + 0.245380i 0.697219 0.716858i \(-0.254421\pi\)
−0.272208 + 0.962238i \(0.587754\pi\)
\(648\) −518.949 161.051i −0.800846 0.248536i
\(649\) 112.500 + 194.856i 0.173344 + 0.300240i
\(650\) 89.4427i 0.137604i
\(651\) 42.0000 46.9574i 0.0645161 0.0721312i
\(652\) 2.00000 0.00306748
\(653\) 865.612 499.761i 1.32559 0.765331i 0.340978 0.940071i \(-0.389242\pi\)
0.984615 + 0.174740i \(0.0559086\pi\)
\(654\) −917.710 + 301.545i −1.40323 + 0.461077i
\(655\) 212.500 368.061i 0.324427 0.561925i
\(656\) −515.107 + 297.397i −0.785224 + 0.453349i
\(657\) −18.0000 160.997i −0.0273973 0.245049i
\(658\) −105.000 181.865i −0.159574 0.276391i
\(659\) 657.404i 0.997578i −0.866723 0.498789i \(-0.833778\pi\)
0.866723 0.498789i \(-0.166222\pi\)
\(660\) 73.4123 + 15.3504i 0.111231 + 0.0232582i
\(661\) 418.000 723.997i 0.632375 1.09531i −0.354690 0.934984i \(-0.615413\pi\)
0.987065 0.160322i \(-0.0512532\pi\)
\(662\) −30.9839 17.8885i −0.0468034 0.0270220i
\(663\) −32.9516 + 157.589i −0.0497008 + 0.237690i
\(664\) −945.000 −1.42319
\(665\) −216.887 + 125.220i −0.326146 + 0.188300i
\(666\) −240.000 + 26.8328i −0.360360 + 0.0402895i
\(667\) 105.000 + 181.865i 0.157421 + 0.272662i
\(668\) 216.887 + 125.220i 0.324681 + 0.187455i
\(669\) −100.205 304.959i −0.149783 0.455843i
\(670\) −130.000 225.167i −0.194030 0.336070i
\(671\) 290.689i 0.433217i
\(672\) −245.000 219.135i −0.364583 0.326093i
\(673\) −677.000 −1.00594 −0.502972 0.864303i \(-0.667760\pi\)
−0.502972 + 0.864303i \(0.667760\pi\)
\(674\) 985.674 569.079i 1.46242 0.844331i
\(675\) 491.109 224.526i 0.727569 0.332632i
\(676\) −82.5000 + 142.894i −0.122041 + 0.211382i
\(677\) 923.707 533.302i 1.36441 0.787743i 0.374204 0.927346i \(-0.377916\pi\)
0.990208 + 0.139603i \(0.0445827\pi\)
\(678\) −140.000 + 156.525i −0.206490 + 0.230862i
\(679\) −325.500 + 563.783i −0.479381 + 0.830313i
\(680\) 402.492i 0.591900i
\(681\) −185.353 + 886.436i −0.272177 + 1.30167i
\(682\) −37.5000 + 64.9519i −0.0549853 + 0.0952374i
\(683\) 551.900 + 318.640i 0.808053 + 0.466530i 0.846279 0.532740i \(-0.178837\pi\)
−0.0382264 + 0.999269i \(0.512171\pi\)
\(684\) 115.935 85.4106i 0.169496 0.124869i
\(685\) 480.000 0.700730
\(686\) 664.217 383.486i 0.968246 0.559017i
\(687\) −668.000 + 746.847i −0.972344 + 1.08711i
\(688\) 418.000 + 723.997i 0.607558 + 1.05232i
\(689\) 34.8569 + 20.1246i 0.0505905 + 0.0292084i
\(690\) −191.190 + 62.8218i −0.277086 + 0.0910460i
\(691\) −337.000 583.701i −0.487699 0.844719i 0.512201 0.858866i \(-0.328830\pi\)
−0.999900 + 0.0141462i \(0.995497\pi\)
\(692\) 263.856i 0.381295i
\(693\) −282.223 + 645.349i −0.407248 + 0.931239i
\(694\) 850.000 1.22478
\(695\) −220.760 + 127.456i −0.317640 + 0.183390i
\(696\) 98.3316 + 299.259i 0.141281 + 0.429970i
\(697\) 420.000 727.461i 0.602582 1.04370i
\(698\) −1216.12 + 702.125i −1.74229 + 1.00591i
\(699\) −600.000 536.656i −0.858369 0.767749i
\(700\) 140.000 0.200000
\(701\) 1080.02i 1.54069i 0.637630 + 0.770343i \(0.279915\pi\)
−0.637630 + 0.770343i \(0.720085\pi\)
\(702\) −120.206 11.4283i −0.171233 0.0162796i
\(703\) −96.0000 + 166.277i −0.136558 + 0.236525i
\(704\) −396.981 229.197i −0.563893 0.325564i
\(705\) −88.0948 18.4205i −0.124957 0.0261284i
\(706\) 1040.00 1.47309
\(707\) −352.441 + 203.482i −0.498503 + 0.287811i
\(708\) 45.0000 + 40.2492i 0.0635593 + 0.0568492i
\(709\) 57.0000 + 98.7269i 0.0803949 + 0.139248i 0.903420 0.428757i \(-0.141049\pi\)
−0.823025 + 0.568006i \(0.807715\pi\)
\(710\) −406.663 234.787i −0.572765 0.330686i
\(711\) −651.431 284.883i −0.916219 0.400679i
\(712\) −165.000 285.788i −0.231742 0.401388i
\(713\) 40.2492i 0.0564505i
\(714\) 1233.33 + 257.887i 1.72735 + 0.361186i
\(715\) −50.0000 −0.0699301
\(716\) −166.538 + 96.1509i −0.232595 + 0.134289i
\(717\) 802.996 263.851i 1.11994 0.367994i
\(718\) −260.000 + 450.333i −0.362117 + 0.627205i
\(719\) −336.950 + 194.538i −0.468636 + 0.270567i −0.715669 0.698440i \(-0.753878\pi\)
0.247032 + 0.969007i \(0.420545\pi\)
\(720\) −380.000 + 42.4853i −0.527778 + 0.0590073i
\(721\) 574.000 0.796117
\(722\) 234.787i 0.325190i
\(723\) −525.632 109.909i −0.727015 0.152018i
\(724\) 41.0000 71.0141i 0.0566298 0.0980858i
\(725\) −271.109 156.525i −0.373943 0.215896i
\(726\) 5.49193 26.2648i 0.00756465 0.0361774i
\(727\) 1307.00 1.79780 0.898900 0.438155i \(-0.144368\pi\)
0.898900 + 0.438155i \(0.144368\pi\)
\(728\) 81.3327 + 46.9574i 0.111721 + 0.0645020i
\(729\) 239.000 + 688.709i 0.327846 + 0.944731i
\(730\) −45.0000 77.9423i −0.0616438 0.106770i
\(731\) −1022.47 590.322i −1.39872 0.807554i
\(732\) 24.3488 + 74.1022i 0.0332634 + 0.101233i
\(733\) −204.000 353.338i −0.278308 0.482044i 0.692656 0.721268i \(-0.256440\pi\)
−0.970964 + 0.239224i \(0.923107\pi\)
\(734\) 1120.27i 1.52625i
\(735\) 67.2762 321.744i 0.0915322 0.437746i
\(736\) −210.000 −0.285326
\(737\) −503.488 + 290.689i −0.683159 + 0.394422i
\(738\) 577.218 + 252.428i 0.782138 + 0.342043i
\(739\) 177.000 306.573i 0.239513 0.414848i −0.721062 0.692871i \(-0.756346\pi\)
0.960575 + 0.278022i \(0.0896789\pi\)
\(740\) −23.2379 + 13.4164i −0.0314026 + 0.0181303i
\(741\) −64.0000 + 71.5542i −0.0863698 + 0.0965643i
\(742\) 157.500 272.798i 0.212264 0.367652i
\(743\) 751.319i 1.01120i −0.862769 0.505598i \(-0.831272\pi\)
0.862769 0.505598i \(-0.168728\pi\)
\(744\) 12.3569 59.0958i 0.0166087 0.0794298i
\(745\) 15.0000 25.9808i 0.0201342 0.0348735i
\(746\) 1351.67 + 780.388i 1.81189 + 1.04610i
\(747\) 751.999 + 1020.76i 1.00669 + 1.36647i
\(748\) −300.000 −0.401070
\(749\) 453.922i 0.606037i
\(750\) 450.000 503.115i 0.600000 0.670820i
\(751\) 515.500 + 892.872i 0.686418 + 1.18891i 0.972989 + 0.230852i \(0.0741513\pi\)
−0.286571 + 0.958059i \(0.592515\pi\)
\(752\) −220.760 127.456i −0.293564 0.169489i
\(753\) 490.720 161.243i 0.651686 0.214134i
\(754\) 35.0000 + 60.6218i 0.0464191 + 0.0804002i
\(755\) 131.928i 0.174739i
\(756\) −17.8881 + 188.152i −0.0236615 + 0.248878i
\(757\) −1258.00 −1.66182 −0.830911 0.556405i \(-0.812180\pi\)
−0.830911 + 0.556405i \(0.812180\pi\)
\(758\) −708.756 + 409.200i −0.935034 + 0.539842i
\(759\) 140.474 + 427.513i 0.185077 + 0.563258i
\(760\) −120.000 + 207.846i −0.157895 + 0.273482i
\(761\) 801.708 462.866i 1.05349 0.608234i 0.129867 0.991531i \(-0.458545\pi\)
0.923625 + 0.383297i \(0.125212\pi\)
\(762\) −885.000 791.568i −1.16142 1.03880i
\(763\) −504.000 872.954i −0.660550 1.14411i
\(764\) 169.941i 0.222436i
\(765\) 434.758 320.290i 0.568311 0.418679i
\(766\) 15.0000 25.9808i 0.0195822 0.0339174i
\(767\) −34.8569 20.1246i −0.0454457 0.0262381i
\(768\) −531.505 111.137i −0.692064 0.144710i
\(769\) −877.000 −1.14044 −0.570221 0.821491i \(-0.693142\pi\)
−0.570221 + 0.821491i \(0.693142\pi\)
\(770\) 391.312i 0.508197i
\(771\) −590.000 527.712i −0.765240 0.684451i
\(772\) 29.5000 + 51.0955i 0.0382124 + 0.0661859i
\(773\) 437.647 + 252.676i 0.566167 + 0.326877i 0.755617 0.655014i \(-0.227337\pi\)
−0.189450 + 0.981890i \(0.560670\pi\)
\(774\) 354.794 811.296i 0.458391 1.04819i
\(775\) 30.0000 + 51.9615i 0.0387097 + 0.0670471i
\(776\) 623.863i 0.803947i
\(777\) −78.6653 239.407i −0.101242 0.308117i
\(778\) 150.000 0.192802
\(779\) 433.774 250.440i 0.556835 0.321489i
\(780\) −12.7460 + 4.18812i −0.0163410 + 0.00536938i
\(781\) −525.000 + 909.327i −0.672215 + 1.16431i
\(782\) 697.137 402.492i 0.891480 0.514696i
\(783\) 245.000 344.354i 0.312899 0.439789i
\(784\) 465.500 806.270i 0.593750 1.02841i
\(785\) 554.545i 0.706427i
\(786\) −1248.01 260.957i −1.58780 0.332007i
\(787\) −611.000 + 1058.28i −0.776366 + 1.34471i 0.157658 + 0.987494i \(0.449606\pi\)
−0.934024 + 0.357211i \(0.883728\pi\)
\(788\) −189.776 109.567i −0.240833 0.139045i
\(789\) 21.9677 105.059i 0.0278425 0.133155i
\(790\) −395.000 −0.500000
\(791\) −189.776 109.567i −0.239919 0.138517i
\(792\) 75.0000 + 670.820i 0.0946970 + 0.846995i
\(793\) −26.0000 45.0333i −0.0327869 0.0567886i
\(794\) −511.234 295.161i −0.643871 0.371739i
\(795\) −42.1421 128.254i −0.0530090 0.161326i
\(796\) −117.000 202.650i −0.146985 0.254585i
\(797\) 547.837i 0.687373i −0.939084 0.343687i \(-0.888324\pi\)
0.939084 0.343687i \(-0.111676\pi\)
\(798\) 560.000 + 500.879i 0.701754 + 0.627668i
\(799\) 360.000 0.450563
\(800\) 271.109 156.525i 0.338886 0.195656i
\(801\) −177.397 + 405.648i −0.221470 + 0.506427i
\(802\) −120.000 + 207.846i −0.149626 + 0.259160i
\(803\) −174.284 + 100.623i −0.217041 + 0.125309i
\(804\) −104.000 + 116.276i −0.129353 + 0.144621i
\(805\) −105.000 181.865i −0.130435 0.225920i
\(806\) 13.4164i 0.0166457i
\(807\) −243.018 + 1162.22i −0.301138 + 1.44017i
\(808\) −195.000 + 337.750i −0.241337 + 0.418007i
\(809\) 185.903 + 107.331i 0.229794 + 0.132672i 0.610477 0.792034i \(-0.290978\pi\)
−0.380683 + 0.924706i \(0.624311\pi\)
\(810\) 274.960 + 297.359i 0.339456 + 0.367109i
\(811\) −436.000 −0.537608 −0.268804 0.963195i \(-0.586628\pi\)
−0.268804 + 0.963195i \(0.586628\pi\)
\(812\) 94.8881 54.7837i 0.116857 0.0674676i
\(813\) 914.000 1021.88i 1.12423 1.25693i
\(814\) 150.000 + 259.808i 0.184275 + 0.319174i
\(815\) 3.87298 + 2.23607i 0.00475213 + 0.00274364i
\(816\) 1453.04 477.445i 1.78069 0.585105i
\(817\) −352.000 609.682i −0.430845 0.746245i
\(818\) 444.978i 0.543982i
\(819\) −14.0000 125.220i −0.0170940 0.152894i
\(820\) 70.0000 0.0853659
\(821\) 404.727 233.669i 0.492968 0.284615i −0.232837 0.972516i \(-0.574801\pi\)
0.725805 + 0.687901i \(0.241467\pi\)
\(822\) −449.516 1368.04i −0.546856 1.66428i
\(823\) 261.000 452.065i 0.317132 0.549290i −0.662756 0.748835i \(-0.730613\pi\)
0.979888 + 0.199546i \(0.0639467\pi\)
\(824\) 476.377 275.036i 0.578127 0.333782i
\(825\) −500.000 447.214i −0.606061 0.542077i
\(826\) −157.500 + 272.798i −0.190678 + 0.330264i
\(827\) 986.106i 1.19239i −0.802840 0.596195i \(-0.796679\pi\)
0.802840 0.596195i \(-0.203321\pi\)
\(828\) 71.6190 + 97.2148i 0.0864963 + 0.117409i
\(829\) 152.000 263.272i 0.183353 0.317577i −0.759667 0.650312i \(-0.774638\pi\)
0.943020 + 0.332735i \(0.107971\pi\)
\(830\) 609.995 + 352.181i 0.734934 + 0.424314i
\(831\) −152.698 31.9289i −0.183752 0.0384222i
\(832\) 82.0000 0.0985577
\(833\) 1314.81i 1.57840i
\(834\) 570.000 + 509.823i 0.683453 + 0.611299i
\(835\) 280.000 + 484.974i 0.335329 + 0.580807i
\(836\) −154.919 89.4427i −0.185310 0.106989i
\(837\) −73.6663 + 33.6790i −0.0880123 + 0.0402377i
\(838\) 105.000 + 181.865i 0.125298 + 0.217023i
\(839\) 1001.76i 1.19399i 0.802245 + 0.596996i \(0.203639\pi\)
−0.802245 + 0.596996i \(0.796361\pi\)
\(840\) −98.3316 299.259i −0.117061 0.356261i
\(841\) 596.000 0.708680
\(842\) −491.869 + 283.981i −0.584167 + 0.337269i
\(843\) −356.887 + 117.267i −0.423354 + 0.139107i
\(844\) −13.0000 + 22.5167i −0.0154028 + 0.0266785i
\(845\) −319.521 + 184.476i −0.378132 + 0.218314i
\(846\) 30.0000 + 268.328i 0.0354610 + 0.317173i
\(847\) 28.0000 0.0330579
\(848\) 382.368i 0.450905i
\(849\) −258.411 54.0335i −0.304371 0.0636437i
\(850\) −600.000 + 1039.23i −0.705882 + 1.22262i
\(851\) −139.427 80.4984i −0.163839 0.0945928i
\(852\) −57.6653 + 275.780i −0.0676823 + 0.323686i
\(853\) 824.000 0.966002 0.483001 0.875620i \(-0.339547\pi\)
0.483001 + 0.875620i \(0.339547\pi\)
\(854\) −352.441 + 203.482i −0.412695 + 0.238270i
\(855\) 320.000 35.7771i 0.374269 0.0418445i
\(856\) 217.500 + 376.721i 0.254089 + 0.440095i
\(857\) 3.87298 + 2.23607i 0.00451923 + 0.00260918i 0.502258 0.864718i \(-0.332503\pi\)
−0.497739 + 0.867327i \(0.665836\pi\)
\(858\) 46.8246 + 142.504i 0.0545741 + 0.166089i
\(859\) −64.0000 110.851i −0.0745052 0.129047i 0.826366 0.563134i \(-0.190404\pi\)
−0.900871 + 0.434087i \(0.857071\pi\)
\(860\) 98.3870i 0.114403i
\(861\) −134.552 + 643.487i −0.156275 + 0.747372i
\(862\) −270.000 −0.313225
\(863\) −1289.70 + 744.611i −1.49444 + 0.862816i −0.999980 0.00638254i \(-0.997968\pi\)
−0.494462 + 0.869199i \(0.664635\pi\)
\(864\) 175.720 + 384.353i 0.203379 + 0.444854i
\(865\) −295.000 + 510.955i −0.341040 + 0.590699i
\(866\) 979.865 565.725i 1.13148 0.653262i
\(867\) −862.000 + 963.745i −0.994233 + 1.11159i
\(868\) −21.0000 −0.0241935
\(869\) 883.247i 1.01639i
\(870\) 48.0544 229.817i 0.0552350 0.264157i
\(871\) 52.0000 90.0666i 0.0597015 0.103406i
\(872\) −836.564 482.991i −0.959363 0.553888i
\(873\) 673.875 496.449i 0.771907 0.568670i
\(874\) 480.000 0.549199
\(875\) 609.995 + 352.181i 0.697137 + 0.402492i
\(876\) −36.0000 + 40.2492i −0.0410959 + 0.0459466i
\(877\) −776.000 1344.07i −0.884835 1.53258i −0.845903 0.533337i \(-0.820938\pi\)
−0.0389316 0.999242i \(-0.512395\pi\)
\(878\) 912.088 + 526.594i 1.03882 + 0.599765i
\(879\) 44.6109 14.6584i 0.0507519 0.0166762i
\(880\) 237.500 + 411.362i 0.269886 + 0.467457i
\(881\) 1690.47i 1.91881i −0.282040 0.959403i \(-0.591011\pi\)
0.282040 0.959403i \(-0.408989\pi\)
\(882\) −980.000 + 109.567i −1.11111 + 0.124226i
\(883\) −502.000 −0.568516 −0.284258 0.958748i \(-0.591747\pi\)
−0.284258 + 0.958748i \(0.591747\pi\)
\(884\) 46.4758 26.8328i 0.0525744 0.0303539i
\(885\) 42.1421 + 128.254i 0.0476182 + 0.144920i
\(886\) −67.5000 + 116.913i −0.0761851 + 0.131956i
\(887\) −1204.50 + 695.417i −1.35795 + 0.784010i −0.989347 0.145578i \(-0.953496\pi\)
−0.368599 + 0.929589i \(0.620162\pi\)
\(888\) −180.000 160.997i −0.202703 0.181303i
\(889\) 619.500 1073.01i 0.696850 1.20698i
\(890\) 245.967i 0.276368i
\(891\) 664.914 614.829i 0.746256 0.690043i
\(892\) −53.5000 + 92.6647i −0.0599776 + 0.103884i
\(893\) 185.903 + 107.331i 0.208178 + 0.120192i
\(894\) −88.0948 18.4205i −0.0985400 0.0206046i
\(895\) −430.000 −0.480447
\(896\) 1080.02i 1.20538i
\(897\) −60.0000 53.6656i −0.0668896 0.0598279i
\(898\) 315.000 + 545.596i 0.350780 + 0.607568i
\(899\) 40.6663 + 23.4787i 0.0452351 + 0.0261165i
\(900\) −164.919 72.1222i −0.183244 0.0801358i
\(901\) 270.000 + 467.654i 0.299667 + 0.519039i
\(902\) 782.624i 0.867654i
\(903\) 904.439 + 189.117i 1.00159 + 0.209432i
\(904\) −210.000 −0.232301
\(905\) 158.792 91.6788i 0.175461 0.101303i
\(906\) 376.006 123.549i 0.415018 0.136368i
\(907\) 149.000 258.076i 0.164278 0.284538i −0.772121 0.635476i \(-0.780804\pi\)
0.936399 + 0.350938i \(0.114137\pi\)
\(908\) 261.426 150.935i 0.287915 0.166228i
\(909\) 520.000 58.1378i 0.572057 0.0639579i
\(910\) −35.0000 60.6218i −0.0384615 0.0666173i
\(911\) 657.404i 0.721629i 0.932638 + 0.360814i \(0.117501\pi\)
−0.932638 + 0.360814i \(0.882499\pi\)
\(912\) 892.693 + 186.661i 0.978831 + 0.204672i
\(913\) 787.500 1363.99i 0.862541 1.49396i
\(914\) −44.5393 25.7148i −0.0487301 0.0281343i
\(915\) −35.6976 + 170.721i −0.0390137 + 0.186580i
\(916\) 334.000 0.364629
\(917\) 1330.46i 1.45088i
\(918\) −1320.00 939.149i −1.43791 1.02304i
\(919\) −139.000 240.755i −0.151251 0.261975i 0.780436 0.625235i \(-0.214997\pi\)
−0.931688 + 0.363260i \(0.881664\pi\)
\(920\) −174.284 100.623i −0.189439 0.109373i
\(921\) 155.458 + 473.114i 0.168792 + 0.513696i
\(922\) −665.000 1151.81i −0.721258 1.24926i
\(923\) 187.830i 0.203499i
\(924\) 223.054 73.2921i 0.241401 0.0793204i
\(925\) 240.000 0.259459
\(926\) −112.317 + 64.8460i −0.121292 + 0.0700280i
\(927\) −676.169 295.701i −0.729417 0.318987i
\(928\) 122.500 212.176i 0.132004 0.228638i
\(929\) −960.500 + 554.545i −1.03391 + 0.596927i −0.918102 0.396345i \(-0.870278\pi\)
−0.115806 + 0.993272i \(0.536945\pi\)
\(930\) −30.0000 + 33.5410i −0.0322581 + 0.0360656i
\(931\) −392.000 + 678.964i −0.421053 + 0.729285i
\(932\) 268.328i 0.287906i
\(933\) 189.472 906.135i 0.203078 0.971206i
\(934\) 645.000 1117.17i 0.690578 1.19612i
\(935\) −580.948 335.410i −0.621334 0.358727i
\(936\) −71.6190 97.2148i −0.0765160 0.103862i
\(937\) −219.000 −0.233725 −0.116862 0.993148i \(-0.537284\pi\)
−0.116862 + 0.993148i \(0.537284\pi\)
\(938\) −704.883 406.964i −0.751474 0.433864i
\(939\) −542.000 + 605.974i −0.577210 + 0.645340i
\(940\) 15.0000 + 25.9808i 0.0159574 + 0.0276391i
\(941\) 884.977 + 510.942i 0.940464 + 0.542977i 0.890106 0.455754i \(-0.150630\pi\)
0.0503583 + 0.998731i \(0.483964\pi\)
\(942\) −1580.50 + 519.327i −1.67781 + 0.551302i
\(943\) 210.000 + 363.731i 0.222694 + 0.385717i
\(944\) 382.368i 0.405050i
\(945\) −245.000 + 344.354i −0.259259 + 0.364396i
\(946\) −1100.00 −1.16279
\(947\) 770.724 444.978i 0.813858 0.469881i −0.0344357 0.999407i \(-0.510963\pi\)
0.848294 + 0.529526i \(0.177630\pi\)
\(948\) 73.9828 + 225.157i 0.0780410 + 0.237507i
\(949\) 18.0000 31.1769i 0.0189673 0.0328524i
\(950\) −619.677 + 357.771i −0.652292 + 0.376601i
\(951\) 975.000 + 872.067i 1.02524 + 0.916999i
\(952\) 630.000 + 1091.19i 0.661765 + 1.14621i
\(953\) 500.879i 0.525582i 0.964853 + 0.262791i \(0.0846429\pi\)
−0.964853 + 0.262791i \(0.915357\pi\)
\(954\) −326.069 + 240.217i −0.341791 + 0.251800i
\(955\) 190.000 329.090i 0.198953 0.344596i
\(956\) −243.998 140.872i −0.255228 0.147356i
\(957\) −513.886 107.453i −0.536976 0.112281i
\(958\) 760.000 0.793319
\(959\) 1301.32 751.319i 1.35696 0.783440i
\(960\) −205.000 183.358i −0.213542 0.190997i
\(961\) 476.000 + 824.456i 0.495317 + 0.857915i
\(962\) −46.4758 26.8328i −0.0483116 0.0278927i
\(963\) 233.842 534.718i 0.242826 0.555262i
\(964\) 89.5000 + 155.019i 0.0928423 + 0.160808i
\(965\) 131.928i 0.136713i
\(966\) −420.000 + 469.574i −0.434783 + 0.486102i
\(967\) 1087.00 1.12410 0.562048 0.827105i \(-0.310014\pi\)
0.562048 + 0.827105i \(0.310014\pi\)
\(968\) 23.2379 13.4164i 0.0240061 0.0138599i
\(969\) −1223.61 + 402.059i −1.26276 + 0.414922i
\(970\) 232.500 402.702i 0.239691 0.415157i
\(971\) 517.043 298.515i 0.532485 0.307431i −0.209543 0.977800i \(-0.567197\pi\)
0.742028 + 0.670369i \(0.233864\pi\)
\(972\) 118.000 212.426i 0.121399 0.218546i
\(973\) −399.000 + 691.088i −0.410072 + 0.710265i
\(974\) 1808.98i 1.85727i
\(975\) 117.460 + 24.5607i 0.120471 + 0.0251904i
\(976\) −247.000 + 427.817i −0.253074 + 0.438337i
\(977\) 511.234 + 295.161i 0.523269 + 0.302109i 0.738271 0.674504i \(-0.235643\pi\)
−0.215002 + 0.976614i \(0.568976\pi\)
\(978\) 2.74597 13.1324i 0.00280774 0.0134278i
\(979\) 550.000 0.561798
\(980\) −94.8881 + 54.7837i −0.0968246 + 0.0559017i
\(981\) 144.000 + 1287.98i 0.146789 + 1.31292i
\(982\) −507.500 879.016i −0.516802 0.895128i
\(983\) 871.421 + 503.115i 0.886492 + 0.511816i 0.872793 0.488090i \(-0.162306\pi\)
0.0136983 + 0.999906i \(0.495640\pi\)
\(984\) 196.663 + 598.518i 0.199861 + 0.608250i
\(985\) −245.000 424.352i −0.248731 0.430815i
\(986\) 939.149i 0.952483i
\(987\) −267.665 + 87.9505i −0.271191 + 0.0891089i
\(988\) 32.0000 0.0323887
\(989\) 511.234 295.161i 0.516920 0.298444i
\(990\) 201.588 460.964i 0.203624 0.465620i
\(991\) −8.50000 + 14.7224i −0.00857719 + 0.0148561i −0.870282 0.492554i \(-0.836064\pi\)
0.861705 + 0.507410i \(0.169397\pi\)
\(992\) −40.6663 + 23.4787i −0.0409943 + 0.0236681i
\(993\) −32.0000 + 35.7771i −0.0322256 + 0.0360293i
\(994\) −1470.00 −1.47887
\(995\) 523.240i 0.525869i
\(996\) 86.4980 413.670i 0.0868453 0.415332i
\(997\) −296.000 + 512.687i −0.296891 + 0.514230i −0.975423 0.220341i \(-0.929283\pi\)
0.678532 + 0.734571i \(0.262616\pi\)
\(998\) −491.869 283.981i −0.492855 0.284550i
\(999\) −30.6653 + 322.546i −0.0306960 + 0.322868i
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 21.3.h.b.11.1 yes 4
3.2 odd 2 inner 21.3.h.b.11.2 yes 4
4.3 odd 2 336.3.bn.f.305.1 4
7.2 even 3 inner 21.3.h.b.2.2 yes 4
7.3 odd 6 147.3.b.c.50.1 2
7.4 even 3 147.3.b.d.50.1 2
7.5 odd 6 147.3.h.b.128.2 4
7.6 odd 2 147.3.h.b.116.1 4
12.11 even 2 336.3.bn.f.305.2 4
21.2 odd 6 inner 21.3.h.b.2.1 4
21.5 even 6 147.3.h.b.128.1 4
21.11 odd 6 147.3.b.d.50.2 2
21.17 even 6 147.3.b.c.50.2 2
21.20 even 2 147.3.h.b.116.2 4
28.23 odd 6 336.3.bn.f.65.2 4
84.23 even 6 336.3.bn.f.65.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.h.b.2.1 4 21.2 odd 6 inner
21.3.h.b.2.2 yes 4 7.2 even 3 inner
21.3.h.b.11.1 yes 4 1.1 even 1 trivial
21.3.h.b.11.2 yes 4 3.2 odd 2 inner
147.3.b.c.50.1 2 7.3 odd 6
147.3.b.c.50.2 2 21.17 even 6
147.3.b.d.50.1 2 7.4 even 3
147.3.b.d.50.2 2 21.11 odd 6
147.3.h.b.116.1 4 7.6 odd 2
147.3.h.b.116.2 4 21.20 even 2
147.3.h.b.128.1 4 21.5 even 6
147.3.h.b.128.2 4 7.5 odd 6
336.3.bn.f.65.1 4 84.23 even 6
336.3.bn.f.65.2 4 28.23 odd 6
336.3.bn.f.305.1 4 4.3 odd 2
336.3.bn.f.305.2 4 12.11 even 2