Properties

Label 483.2.i.h.277.7
Level $483$
Weight $2$
Character 483.277
Analytic conductor $3.857$
Analytic rank $0$
Dimension $20$
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] = [483,2,Mod(277,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (of order \(3\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + 7135 x^{12} - 6640 x^{11} + 20315 x^{10} - 10565 x^{9} + 29358 x^{8} - 9009 x^{7} + \cdots + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 277.7
Root \(-0.384545 + 0.666052i\) of defining polynomial
Character \(\chi\) \(=\) 483.277
Dual form 483.2.i.h.415.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.384545 + 0.666052i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.704250 - 1.21980i) q^{4} +(2.01355 + 3.48756i) q^{5} +0.769091 q^{6} +(2.63574 - 0.229917i) q^{7} +2.62145 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.384545 + 0.666052i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.704250 - 1.21980i) q^{4} +(2.01355 + 3.48756i) q^{5} +0.769091 q^{6} +(2.63574 - 0.229917i) q^{7} +2.62145 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.54860 + 2.68225i) q^{10} +(-2.73557 + 4.73814i) q^{11} +(-0.704250 - 1.21980i) q^{12} -4.39956 q^{13} +(1.16670 + 1.66713i) q^{14} +4.02709 q^{15} +(-0.400435 - 0.693574i) q^{16} +(1.12483 - 1.94826i) q^{17} +(0.384545 - 0.666052i) q^{18} +(-1.78076 - 3.08437i) q^{19} +5.67216 q^{20} +(1.11876 - 2.39758i) q^{21} -4.20780 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.31072 - 2.27024i) q^{24} +(-5.60873 + 9.71461i) q^{25} +(-1.69183 - 2.93033i) q^{26} -1.00000 q^{27} +(1.57577 - 3.37699i) q^{28} -4.70941 q^{29} +(1.54860 + 2.68225i) q^{30} +(5.27462 - 9.13592i) q^{31} +(2.92942 - 5.07390i) q^{32} +(2.73557 + 4.73814i) q^{33} +1.73019 q^{34} +(6.10904 + 8.72937i) q^{35} -1.40850 q^{36} +(1.96275 + 3.39958i) q^{37} +(1.36957 - 2.37216i) q^{38} +(-2.19978 + 3.81013i) q^{39} +(5.27840 + 9.14246i) q^{40} -3.97807 q^{41} +(2.02712 - 0.176827i) q^{42} +2.61087 q^{43} +(3.85304 + 6.67367i) q^{44} +(2.01355 - 3.48756i) q^{45} +(0.384545 - 0.666052i) q^{46} +(0.259175 + 0.448904i) q^{47} -0.800870 q^{48} +(6.89428 - 1.21200i) q^{49} -8.62724 q^{50} +(-1.12483 - 1.94826i) q^{51} +(-3.09839 + 5.36656i) q^{52} +(6.31816 - 10.9434i) q^{53} +(-0.384545 - 0.666052i) q^{54} -22.0328 q^{55} +(6.90945 - 0.602714i) q^{56} -3.56152 q^{57} +(-1.81098 - 3.13671i) q^{58} +(-0.421445 + 0.729964i) q^{59} +(2.83608 - 4.91223i) q^{60} +(-4.50466 - 7.80230i) q^{61} +8.11333 q^{62} +(-1.51698 - 2.16766i) q^{63} +2.90423 q^{64} +(-8.85871 - 15.3437i) q^{65} +(-2.10390 + 3.64406i) q^{66} +(0.699842 - 1.21216i) q^{67} +(-1.58432 - 2.74412i) q^{68} -1.00000 q^{69} +(-3.46501 + 7.42577i) q^{70} -7.10801 q^{71} +(-1.31072 - 2.27024i) q^{72} +(-2.66304 + 4.61252i) q^{73} +(-1.50953 + 2.61458i) q^{74} +(5.60873 + 9.71461i) q^{75} -5.01640 q^{76} +(-6.12087 + 13.1175i) q^{77} -3.38366 q^{78} +(6.72171 + 11.6423i) q^{79} +(1.61259 - 2.79309i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.52975 - 2.64960i) q^{82} +3.39713 q^{83} +(-2.13667 - 3.05315i) q^{84} +9.05955 q^{85} +(1.00400 + 1.73898i) q^{86} +(-2.35471 + 4.07847i) q^{87} +(-7.17114 + 12.4208i) q^{88} +(-6.50780 - 11.2718i) q^{89} +3.09720 q^{90} +(-11.5961 + 1.01153i) q^{91} -1.40850 q^{92} +(-5.27462 - 9.13592i) q^{93} +(-0.199329 + 0.345248i) q^{94} +(7.17128 - 12.4210i) q^{95} +(-2.92942 - 5.07390i) q^{96} -6.35615 q^{97} +(3.45842 + 4.12588i) q^{98} +5.47113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.384545 + 0.666052i 0.271915 + 0.470970i 0.969352 0.245676i \(-0.0790098\pi\)
−0.697437 + 0.716646i \(0.745677\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.704250 1.21980i 0.352125 0.609898i
\(5\) 2.01355 + 3.48756i 0.900485 + 1.55969i 0.826866 + 0.562399i \(0.190122\pi\)
0.0736191 + 0.997286i \(0.476545\pi\)
\(6\) 0.769091 0.313980
\(7\) 2.63574 0.229917i 0.996217 0.0869003i
\(8\) 2.62145 0.926821
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.54860 + 2.68225i −0.489710 + 0.848203i
\(11\) −2.73557 + 4.73814i −0.824804 + 1.42860i 0.0772644 + 0.997011i \(0.475381\pi\)
−0.902069 + 0.431592i \(0.857952\pi\)
\(12\) −0.704250 1.21980i −0.203299 0.352125i
\(13\) −4.39956 −1.22022 −0.610109 0.792318i \(-0.708874\pi\)
−0.610109 + 0.792318i \(0.708874\pi\)
\(14\) 1.16670 + 1.66713i 0.311813 + 0.445559i
\(15\) 4.02709 1.03979
\(16\) −0.400435 0.693574i −0.100109 0.173394i
\(17\) 1.12483 1.94826i 0.272810 0.472521i −0.696770 0.717295i \(-0.745380\pi\)
0.969580 + 0.244773i \(0.0787135\pi\)
\(18\) 0.384545 0.666052i 0.0906382 0.156990i
\(19\) −1.78076 3.08437i −0.408534 0.707602i 0.586191 0.810173i \(-0.300627\pi\)
−0.994726 + 0.102570i \(0.967293\pi\)
\(20\) 5.67216 1.26833
\(21\) 1.11876 2.39758i 0.244133 0.523194i
\(22\) −4.20780 −0.897105
\(23\) −0.500000 0.866025i −0.104257 0.180579i
\(24\) 1.31072 2.27024i 0.267550 0.463410i
\(25\) −5.60873 + 9.71461i −1.12175 + 1.94292i
\(26\) −1.69183 2.93033i −0.331795 0.574686i
\(27\) −1.00000 −0.192450
\(28\) 1.57577 3.37699i 0.297792 0.638191i
\(29\) −4.70941 −0.874516 −0.437258 0.899336i \(-0.644050\pi\)
−0.437258 + 0.899336i \(0.644050\pi\)
\(30\) 1.54860 + 2.68225i 0.282734 + 0.489710i
\(31\) 5.27462 9.13592i 0.947350 1.64086i 0.196375 0.980529i \(-0.437083\pi\)
0.750975 0.660330i \(-0.229584\pi\)
\(32\) 2.92942 5.07390i 0.517852 0.896947i
\(33\) 2.73557 + 4.73814i 0.476201 + 0.824804i
\(34\) 1.73019 0.296724
\(35\) 6.10904 + 8.72937i 1.03262 + 1.47553i
\(36\) −1.40850 −0.234750
\(37\) 1.96275 + 3.39958i 0.322673 + 0.558887i 0.981039 0.193812i \(-0.0620851\pi\)
−0.658365 + 0.752699i \(0.728752\pi\)
\(38\) 1.36957 2.37216i 0.222173 0.384815i
\(39\) −2.19978 + 3.81013i −0.352246 + 0.610109i
\(40\) 5.27840 + 9.14246i 0.834588 + 1.44555i
\(41\) −3.97807 −0.621270 −0.310635 0.950529i \(-0.600542\pi\)
−0.310635 + 0.950529i \(0.600542\pi\)
\(42\) 2.02712 0.176827i 0.312792 0.0272849i
\(43\) 2.61087 0.398155 0.199077 0.979984i \(-0.436206\pi\)
0.199077 + 0.979984i \(0.436206\pi\)
\(44\) 3.85304 + 6.67367i 0.580868 + 1.00609i
\(45\) 2.01355 3.48756i 0.300162 0.519895i
\(46\) 0.384545 0.666052i 0.0566981 0.0982040i
\(47\) 0.259175 + 0.448904i 0.0378046 + 0.0654794i 0.884309 0.466903i \(-0.154630\pi\)
−0.846504 + 0.532382i \(0.821297\pi\)
\(48\) −0.800870 −0.115596
\(49\) 6.89428 1.21200i 0.984897 0.173143i
\(50\) −8.62724 −1.22008
\(51\) −1.12483 1.94826i −0.157507 0.272810i
\(52\) −3.09839 + 5.36656i −0.429669 + 0.744208i
\(53\) 6.31816 10.9434i 0.867865 1.50319i 0.00369181 0.999993i \(-0.498825\pi\)
0.864174 0.503194i \(-0.167842\pi\)
\(54\) −0.384545 0.666052i −0.0523300 0.0906382i
\(55\) −22.0328 −2.97090
\(56\) 6.90945 0.602714i 0.923315 0.0805410i
\(57\) −3.56152 −0.471735
\(58\) −1.81098 3.13671i −0.237794 0.411871i
\(59\) −0.421445 + 0.729964i −0.0548675 + 0.0950332i −0.892155 0.451730i \(-0.850807\pi\)
0.837287 + 0.546763i \(0.184140\pi\)
\(60\) 2.83608 4.91223i 0.366136 0.634166i
\(61\) −4.50466 7.80230i −0.576762 0.998982i −0.995848 0.0910347i \(-0.970983\pi\)
0.419085 0.907947i \(-0.362351\pi\)
\(62\) 8.11333 1.03039
\(63\) −1.51698 2.16766i −0.191122 0.273100i
\(64\) 2.90423 0.363029
\(65\) −8.85871 15.3437i −1.09879 1.90316i
\(66\) −2.10390 + 3.64406i −0.258972 + 0.448553i
\(67\) 0.699842 1.21216i 0.0854993 0.148089i −0.820105 0.572214i \(-0.806085\pi\)
0.905604 + 0.424125i \(0.139418\pi\)
\(68\) −1.58432 2.74412i −0.192127 0.332773i
\(69\) −1.00000 −0.120386
\(70\) −3.46501 + 7.42577i −0.414148 + 0.887550i
\(71\) −7.10801 −0.843565 −0.421783 0.906697i \(-0.638596\pi\)
−0.421783 + 0.906697i \(0.638596\pi\)
\(72\) −1.31072 2.27024i −0.154470 0.267550i
\(73\) −2.66304 + 4.61252i −0.311685 + 0.539854i −0.978727 0.205166i \(-0.934227\pi\)
0.667042 + 0.745020i \(0.267560\pi\)
\(74\) −1.50953 + 2.61458i −0.175479 + 0.303939i
\(75\) 5.60873 + 9.71461i 0.647640 + 1.12175i
\(76\) −5.01640 −0.575420
\(77\) −6.12087 + 13.1175i −0.697538 + 1.49487i
\(78\) −3.38366 −0.383124
\(79\) 6.72171 + 11.6423i 0.756251 + 1.30987i 0.944750 + 0.327792i \(0.106305\pi\)
−0.188498 + 0.982073i \(0.560362\pi\)
\(80\) 1.61259 2.79309i 0.180293 0.312277i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.52975 2.64960i −0.168932 0.292600i
\(83\) 3.39713 0.372883 0.186442 0.982466i \(-0.440304\pi\)
0.186442 + 0.982466i \(0.440304\pi\)
\(84\) −2.13667 3.05315i −0.233130 0.333126i
\(85\) 9.05955 0.982646
\(86\) 1.00400 + 1.73898i 0.108264 + 0.187519i
\(87\) −2.35471 + 4.07847i −0.252451 + 0.437258i
\(88\) −7.17114 + 12.4208i −0.764446 + 1.32406i
\(89\) −6.50780 11.2718i −0.689826 1.19481i −0.971894 0.235419i \(-0.924354\pi\)
0.282068 0.959394i \(-0.408980\pi\)
\(90\) 3.09720 0.326473
\(91\) −11.5961 + 1.01153i −1.21560 + 0.106037i
\(92\) −1.40850 −0.146846
\(93\) −5.27462 9.13592i −0.546953 0.947350i
\(94\) −0.199329 + 0.345248i −0.0205592 + 0.0356096i
\(95\) 7.17128 12.4210i 0.735758 1.27437i
\(96\) −2.92942 5.07390i −0.298982 0.517852i
\(97\) −6.35615 −0.645369 −0.322684 0.946507i \(-0.604585\pi\)
−0.322684 + 0.946507i \(0.604585\pi\)
\(98\) 3.45842 + 4.12588i 0.349353 + 0.416777i
\(99\) 5.47113 0.549870
\(100\) 7.89990 + 13.6830i 0.789990 + 1.36830i
\(101\) −1.41794 + 2.45594i −0.141090 + 0.244375i −0.927907 0.372811i \(-0.878394\pi\)
0.786817 + 0.617186i \(0.211727\pi\)
\(102\) 0.865093 1.49838i 0.0856570 0.148362i
\(103\) −5.29469 9.17067i −0.521701 0.903613i −0.999681 0.0252423i \(-0.991964\pi\)
0.477980 0.878371i \(-0.341369\pi\)
\(104\) −11.5332 −1.13092
\(105\) 10.6144 0.925895i 1.03586 0.0903581i
\(106\) 9.71847 0.943941
\(107\) 9.42702 + 16.3281i 0.911344 + 1.57849i 0.812167 + 0.583424i \(0.198288\pi\)
0.0991766 + 0.995070i \(0.468379\pi\)
\(108\) −0.704250 + 1.21980i −0.0677665 + 0.117375i
\(109\) −5.56722 + 9.64271i −0.533243 + 0.923604i 0.466003 + 0.884783i \(0.345694\pi\)
−0.999246 + 0.0388209i \(0.987640\pi\)
\(110\) −8.47259 14.6750i −0.807830 1.39920i
\(111\) 3.92549 0.372591
\(112\) −1.21491 1.73602i −0.114798 0.164038i
\(113\) −1.29979 −0.122274 −0.0611370 0.998129i \(-0.519473\pi\)
−0.0611370 + 0.998129i \(0.519473\pi\)
\(114\) −1.36957 2.37216i −0.128272 0.222173i
\(115\) 2.01355 3.48756i 0.187764 0.325217i
\(116\) −3.31660 + 5.74453i −0.307939 + 0.533366i
\(117\) 2.19978 + 3.81013i 0.203370 + 0.352246i
\(118\) −0.648259 −0.0596771
\(119\) 2.51681 5.39371i 0.230716 0.494441i
\(120\) 10.5568 0.963699
\(121\) −9.46665 16.3967i −0.860604 1.49061i
\(122\) 3.46449 6.00067i 0.313660 0.543275i
\(123\) −1.98904 + 3.44511i −0.179345 + 0.310635i
\(124\) −7.42931 12.8679i −0.667171 1.15557i
\(125\) −25.0383 −2.23949
\(126\) 0.860426 1.84395i 0.0766528 0.164273i
\(127\) −0.0947076 −0.00840394 −0.00420197 0.999991i \(-0.501338\pi\)
−0.00420197 + 0.999991i \(0.501338\pi\)
\(128\) −4.74202 8.21343i −0.419140 0.725971i
\(129\) 1.30544 2.26108i 0.114937 0.199077i
\(130\) 6.81315 11.8007i 0.597553 1.03499i
\(131\) 6.86302 + 11.8871i 0.599625 + 1.03858i 0.992876 + 0.119150i \(0.0380169\pi\)
−0.393251 + 0.919431i \(0.628650\pi\)
\(132\) 7.70609 0.670729
\(133\) −5.40277 7.72017i −0.468480 0.669424i
\(134\) 1.07648 0.0929941
\(135\) −2.01355 3.48756i −0.173298 0.300162i
\(136\) 2.94867 5.10724i 0.252846 0.437943i
\(137\) 0.515909 0.893580i 0.0440771 0.0763437i −0.843145 0.537686i \(-0.819299\pi\)
0.887222 + 0.461342i \(0.152632\pi\)
\(138\) −0.384545 0.666052i −0.0327347 0.0566981i
\(139\) 0.281873 0.0239081 0.0119541 0.999929i \(-0.496195\pi\)
0.0119541 + 0.999929i \(0.496195\pi\)
\(140\) 14.9503 1.30412i 1.26353 0.110218i
\(141\) 0.518350 0.0436530
\(142\) −2.73335 4.73430i −0.229378 0.397294i
\(143\) 12.0353 20.8457i 1.00644 1.74321i
\(144\) −0.400435 + 0.693574i −0.0333696 + 0.0577978i
\(145\) −9.48262 16.4244i −0.787489 1.36397i
\(146\) −4.09623 −0.339007
\(147\) 2.39751 6.57662i 0.197744 0.542430i
\(148\) 5.52905 0.454485
\(149\) 2.85125 + 4.93851i 0.233584 + 0.404579i 0.958860 0.283879i \(-0.0916214\pi\)
−0.725277 + 0.688458i \(0.758288\pi\)
\(150\) −4.31362 + 7.47141i −0.352206 + 0.610038i
\(151\) −1.43814 + 2.49093i −0.117034 + 0.202709i −0.918591 0.395209i \(-0.870672\pi\)
0.801557 + 0.597919i \(0.204005\pi\)
\(152\) −4.66816 8.08550i −0.378638 0.655821i
\(153\) −2.24965 −0.181874
\(154\) −11.0907 + 0.967442i −0.893712 + 0.0779587i
\(155\) 42.4828 3.41230
\(156\) 3.09839 + 5.36656i 0.248069 + 0.429669i
\(157\) −8.37042 + 14.4980i −0.668032 + 1.15707i 0.310422 + 0.950599i \(0.399530\pi\)
−0.978454 + 0.206466i \(0.933804\pi\)
\(158\) −5.16960 + 8.95402i −0.411272 + 0.712343i
\(159\) −6.31816 10.9434i −0.501062 0.867865i
\(160\) 23.5940 1.86527
\(161\) −1.51698 2.16766i −0.119555 0.170836i
\(162\) −0.769091 −0.0604255
\(163\) 0.343687 + 0.595284i 0.0269197 + 0.0466262i 0.879171 0.476506i \(-0.158097\pi\)
−0.852252 + 0.523132i \(0.824764\pi\)
\(164\) −2.80156 + 4.85244i −0.218765 + 0.378912i
\(165\) −11.0164 + 19.0809i −0.857624 + 1.48545i
\(166\) 1.30635 + 2.26267i 0.101392 + 0.175617i
\(167\) −12.4022 −0.959714 −0.479857 0.877347i \(-0.659312\pi\)
−0.479857 + 0.877347i \(0.659312\pi\)
\(168\) 2.93276 6.28512i 0.226267 0.484908i
\(169\) 6.35609 0.488930
\(170\) 3.48381 + 6.03413i 0.267196 + 0.462797i
\(171\) −1.78076 + 3.08437i −0.136178 + 0.235867i
\(172\) 1.83871 3.18473i 0.140200 0.242834i
\(173\) 1.60350 + 2.77735i 0.121912 + 0.211158i 0.920522 0.390691i \(-0.127764\pi\)
−0.798610 + 0.601850i \(0.794431\pi\)
\(174\) −3.62197 −0.274581
\(175\) −12.5496 + 26.8947i −0.948662 + 2.03305i
\(176\) 4.38167 0.330281
\(177\) 0.421445 + 0.729964i 0.0316777 + 0.0548675i
\(178\) 5.00509 8.66907i 0.375147 0.649774i
\(179\) −5.57358 + 9.65373i −0.416589 + 0.721553i −0.995594 0.0937708i \(-0.970108\pi\)
0.579005 + 0.815324i \(0.303441\pi\)
\(180\) −2.83608 4.91223i −0.211389 0.366136i
\(181\) 18.5663 1.38002 0.690011 0.723799i \(-0.257606\pi\)
0.690011 + 0.723799i \(0.257606\pi\)
\(182\) −5.13296 7.33462i −0.380480 0.543678i
\(183\) −9.00931 −0.665988
\(184\) −1.31072 2.27024i −0.0966277 0.167364i
\(185\) −7.90416 + 13.6904i −0.581125 + 1.00654i
\(186\) 4.05666 7.02635i 0.297449 0.515197i
\(187\) 6.15407 + 10.6592i 0.450030 + 0.779475i
\(188\) 0.730096 0.0532477
\(189\) −2.63574 + 0.229917i −0.191722 + 0.0167240i
\(190\) 11.0307 0.800253
\(191\) 11.4693 + 19.8655i 0.829892 + 1.43742i 0.898122 + 0.439746i \(0.144931\pi\)
−0.0682304 + 0.997670i \(0.521735\pi\)
\(192\) 1.45212 2.51514i 0.104797 0.181514i
\(193\) 5.06476 8.77242i 0.364569 0.631453i −0.624138 0.781314i \(-0.714550\pi\)
0.988707 + 0.149862i \(0.0478829\pi\)
\(194\) −2.44423 4.23352i −0.175485 0.303949i
\(195\) −17.7174 −1.26877
\(196\) 3.37690 9.26317i 0.241207 0.661655i
\(197\) −4.51568 −0.321729 −0.160864 0.986977i \(-0.551428\pi\)
−0.160864 + 0.986977i \(0.551428\pi\)
\(198\) 2.10390 + 3.64406i 0.149518 + 0.258972i
\(199\) −10.4038 + 18.0199i −0.737506 + 1.27740i 0.216109 + 0.976369i \(0.430663\pi\)
−0.953615 + 0.301029i \(0.902670\pi\)
\(200\) −14.7030 + 25.4663i −1.03966 + 1.80074i
\(201\) −0.699842 1.21216i −0.0493631 0.0854993i
\(202\) −2.18104 −0.153458
\(203\) −12.4128 + 1.08277i −0.871208 + 0.0759957i
\(204\) −3.16863 −0.221849
\(205\) −8.01003 13.8738i −0.559445 0.968986i
\(206\) 4.07209 7.05308i 0.283716 0.491411i
\(207\) −0.500000 + 0.866025i −0.0347524 + 0.0601929i
\(208\) 1.76174 + 3.05142i 0.122154 + 0.211578i
\(209\) 19.4856 1.34784
\(210\) 4.69840 + 6.71368i 0.324221 + 0.463288i
\(211\) 26.2315 1.80585 0.902925 0.429799i \(-0.141416\pi\)
0.902925 + 0.429799i \(0.141416\pi\)
\(212\) −8.89912 15.4137i −0.611194 1.05862i
\(213\) −3.55400 + 6.15572i −0.243516 + 0.421783i
\(214\) −7.25023 + 12.5578i −0.495615 + 0.858431i
\(215\) 5.25711 + 9.10559i 0.358532 + 0.620996i
\(216\) −2.62145 −0.178367
\(217\) 11.8021 25.2926i 0.801176 1.71698i
\(218\) −8.56339 −0.579986
\(219\) 2.66304 + 4.61252i 0.179951 + 0.311685i
\(220\) −15.5166 + 26.8755i −1.04613 + 1.81194i
\(221\) −4.94873 + 8.57146i −0.332888 + 0.576579i
\(222\) 1.50953 + 2.61458i 0.101313 + 0.175479i
\(223\) −1.20377 −0.0806102 −0.0403051 0.999187i \(-0.512833\pi\)
−0.0403051 + 0.999187i \(0.512833\pi\)
\(224\) 6.55461 14.0470i 0.437949 0.938555i
\(225\) 11.2175 0.747831
\(226\) −0.499829 0.865729i −0.0332481 0.0575874i
\(227\) −7.12657 + 12.3436i −0.473007 + 0.819273i −0.999523 0.0308929i \(-0.990165\pi\)
0.526515 + 0.850166i \(0.323498\pi\)
\(228\) −2.50820 + 4.34433i −0.166110 + 0.287710i
\(229\) −6.17854 10.7015i −0.408289 0.707178i 0.586409 0.810015i \(-0.300541\pi\)
−0.994698 + 0.102837i \(0.967208\pi\)
\(230\) 3.09720 0.204223
\(231\) 8.29963 + 11.8596i 0.546075 + 0.780302i
\(232\) −12.3455 −0.810520
\(233\) −5.99138 10.3774i −0.392508 0.679844i 0.600271 0.799796i \(-0.295059\pi\)
−0.992780 + 0.119952i \(0.961726\pi\)
\(234\) −1.69183 + 2.93033i −0.110598 + 0.191562i
\(235\) −1.04372 + 1.80778i −0.0680849 + 0.117926i
\(236\) 0.593605 + 1.02815i 0.0386404 + 0.0669271i
\(237\) 13.4434 0.873244
\(238\) 4.56032 0.397798i 0.295602 0.0257854i
\(239\) 6.53934 0.422995 0.211497 0.977379i \(-0.432166\pi\)
0.211497 + 0.977379i \(0.432166\pi\)
\(240\) −1.61259 2.79309i −0.104092 0.180293i
\(241\) −0.250032 + 0.433069i −0.0161060 + 0.0278964i −0.873966 0.485987i \(-0.838460\pi\)
0.857860 + 0.513883i \(0.171794\pi\)
\(242\) 7.28071 12.6106i 0.468022 0.810638i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −12.6896 −0.812369
\(245\) 18.1089 + 21.6038i 1.15693 + 1.38022i
\(246\) −3.05950 −0.195066
\(247\) 7.83455 + 13.5698i 0.498501 + 0.863428i
\(248\) 13.8271 23.9493i 0.878024 1.52078i
\(249\) 1.69857 2.94200i 0.107642 0.186442i
\(250\) −9.62835 16.6768i −0.608951 1.05473i
\(251\) 5.10076 0.321957 0.160978 0.986958i \(-0.448535\pi\)
0.160978 + 0.986958i \(0.448535\pi\)
\(252\) −3.71244 + 0.323837i −0.233862 + 0.0203998i
\(253\) 5.47113 0.343967
\(254\) −0.0364194 0.0630802i −0.00228515 0.00395800i
\(255\) 4.52978 7.84580i 0.283666 0.491323i
\(256\) 6.55128 11.3471i 0.409455 0.709197i
\(257\) 4.42971 + 7.67248i 0.276318 + 0.478596i 0.970467 0.241235i \(-0.0775525\pi\)
−0.694149 + 0.719831i \(0.744219\pi\)
\(258\) 2.00800 0.125013
\(259\) 5.95491 + 8.50914i 0.370020 + 0.528732i
\(260\) −24.9550 −1.54764
\(261\) 2.35471 + 4.07847i 0.145753 + 0.252451i
\(262\) −5.27829 + 9.14226i −0.326094 + 0.564811i
\(263\) −13.0804 + 22.6559i −0.806573 + 1.39703i 0.108651 + 0.994080i \(0.465347\pi\)
−0.915224 + 0.402945i \(0.867987\pi\)
\(264\) 7.17114 + 12.4208i 0.441353 + 0.764446i
\(265\) 50.8876 3.12600
\(266\) 3.06442 6.56728i 0.187892 0.402666i
\(267\) −13.0156 −0.796542
\(268\) −0.985728 1.70733i −0.0602129 0.104292i
\(269\) 7.87844 13.6459i 0.480357 0.832002i −0.519389 0.854538i \(-0.673841\pi\)
0.999746 + 0.0225354i \(0.00717385\pi\)
\(270\) 1.54860 2.68225i 0.0942447 0.163237i
\(271\) 2.97558 + 5.15386i 0.180754 + 0.313075i 0.942137 0.335227i \(-0.108813\pi\)
−0.761384 + 0.648302i \(0.775480\pi\)
\(272\) −1.80168 −0.109243
\(273\) −4.92204 + 10.5483i −0.297895 + 0.638411i
\(274\) 0.793561 0.0479408
\(275\) −30.6861 53.1499i −1.85044 3.20506i
\(276\) −0.704250 + 1.21980i −0.0423909 + 0.0734231i
\(277\) −7.61827 + 13.1952i −0.457738 + 0.792825i −0.998841 0.0481311i \(-0.984673\pi\)
0.541103 + 0.840956i \(0.318007\pi\)
\(278\) 0.108393 + 0.187742i 0.00650097 + 0.0112600i
\(279\) −10.5492 −0.631567
\(280\) 16.0145 + 22.8836i 0.957050 + 1.36755i
\(281\) 1.78254 0.106338 0.0531688 0.998586i \(-0.483068\pi\)
0.0531688 + 0.998586i \(0.483068\pi\)
\(282\) 0.199329 + 0.345248i 0.0118699 + 0.0205592i
\(283\) 9.99956 17.3197i 0.594412 1.02955i −0.399218 0.916856i \(-0.630718\pi\)
0.993630 0.112696i \(-0.0359485\pi\)
\(284\) −5.00581 + 8.67032i −0.297040 + 0.514489i
\(285\) −7.17128 12.4210i −0.424790 0.735758i
\(286\) 18.5124 1.09466
\(287\) −10.4852 + 0.914624i −0.618920 + 0.0539886i
\(288\) −5.85883 −0.345235
\(289\) 5.96953 + 10.3395i 0.351149 + 0.608208i
\(290\) 7.29299 12.6318i 0.428259 0.741767i
\(291\) −3.17807 + 5.50458i −0.186302 + 0.322684i
\(292\) 3.75089 + 6.49673i 0.219504 + 0.380192i
\(293\) −17.4319 −1.01838 −0.509191 0.860653i \(-0.670055\pi\)
−0.509191 + 0.860653i \(0.670055\pi\)
\(294\) 5.30232 0.932139i 0.309238 0.0543635i
\(295\) −3.39439 −0.197629
\(296\) 5.14523 + 8.91180i 0.299060 + 0.517988i
\(297\) 2.73557 4.73814i 0.158734 0.274935i
\(298\) −2.19287 + 3.79816i −0.127030 + 0.220022i
\(299\) 2.19978 + 3.81013i 0.127216 + 0.220345i
\(300\) 15.7998 0.912201
\(301\) 6.88159 0.600283i 0.396648 0.0345997i
\(302\) −2.21212 −0.127293
\(303\) 1.41794 + 2.45594i 0.0814582 + 0.141090i
\(304\) −1.42616 + 2.47018i −0.0817958 + 0.141674i
\(305\) 18.1407 31.4206i 1.03873 1.79914i
\(306\) −0.865093 1.49838i −0.0494541 0.0856570i
\(307\) −22.1407 −1.26363 −0.631817 0.775117i \(-0.717691\pi\)
−0.631817 + 0.775117i \(0.717691\pi\)
\(308\) 11.6900 + 16.7042i 0.666101 + 0.951810i
\(309\) −10.5894 −0.602409
\(310\) 16.3366 + 28.2957i 0.927854 + 1.60709i
\(311\) 3.44517 5.96722i 0.195358 0.338370i −0.751660 0.659551i \(-0.770746\pi\)
0.947018 + 0.321181i \(0.104080\pi\)
\(312\) −5.76660 + 9.98804i −0.326469 + 0.565461i
\(313\) −6.78694 11.7553i −0.383620 0.664450i 0.607956 0.793970i \(-0.291990\pi\)
−0.991577 + 0.129520i \(0.958656\pi\)
\(314\) −12.8752 −0.726591
\(315\) 4.50534 9.65527i 0.253847 0.544013i
\(316\) 18.9350 1.06518
\(317\) 12.3294 + 21.3551i 0.692486 + 1.19942i 0.971021 + 0.238995i \(0.0768181\pi\)
−0.278534 + 0.960426i \(0.589849\pi\)
\(318\) 4.85923 8.41644i 0.272492 0.471971i
\(319\) 12.8829 22.3139i 0.721305 1.24934i
\(320\) 5.84780 + 10.1287i 0.326902 + 0.566211i
\(321\) 18.8540 1.05233
\(322\) 0.860426 1.84395i 0.0479497 0.102760i
\(323\) −8.01218 −0.445810
\(324\) 0.704250 + 1.21980i 0.0391250 + 0.0677665i
\(325\) 24.6759 42.7400i 1.36877 2.37079i
\(326\) −0.264327 + 0.457827i −0.0146397 + 0.0253567i
\(327\) 5.56722 + 9.64271i 0.307868 + 0.533243i
\(328\) −10.4283 −0.575806
\(329\) 0.786329 + 1.12361i 0.0433517 + 0.0619465i
\(330\) −16.9452 −0.932802
\(331\) −11.4838 19.8905i −0.631207 1.09328i −0.987305 0.158834i \(-0.949227\pi\)
0.356099 0.934448i \(-0.384107\pi\)
\(332\) 2.39243 4.14381i 0.131302 0.227421i
\(333\) 1.96275 3.39958i 0.107558 0.186296i
\(334\) −4.76922 8.26054i −0.260960 0.451997i
\(335\) 5.63666 0.307963
\(336\) −2.11089 + 0.184133i −0.115158 + 0.0100453i
\(337\) −19.9238 −1.08532 −0.542659 0.839953i \(-0.682582\pi\)
−0.542659 + 0.839953i \(0.682582\pi\)
\(338\) 2.44420 + 4.23349i 0.132947 + 0.230271i
\(339\) −0.649896 + 1.12565i −0.0352975 + 0.0611370i
\(340\) 6.38019 11.0508i 0.346014 0.599314i
\(341\) 28.8582 + 49.9838i 1.56276 + 2.70678i
\(342\) −2.73913 −0.148115
\(343\) 17.8929 4.77963i 0.966125 0.258076i
\(344\) 6.84426 0.369018
\(345\) −2.01355 3.48756i −0.108406 0.187764i
\(346\) −1.23324 + 2.13603i −0.0662994 + 0.114834i
\(347\) −6.31573 + 10.9392i −0.339046 + 0.587246i −0.984254 0.176762i \(-0.943438\pi\)
0.645207 + 0.764008i \(0.276771\pi\)
\(348\) 3.31660 + 5.74453i 0.177789 + 0.307939i
\(349\) 14.9697 0.801308 0.400654 0.916229i \(-0.368783\pi\)
0.400654 + 0.916229i \(0.368783\pi\)
\(350\) −22.7392 + 1.98355i −1.21546 + 0.106025i
\(351\) 4.39956 0.234831
\(352\) 16.0272 + 27.7600i 0.854254 + 1.47961i
\(353\) −1.36603 + 2.36603i −0.0727064 + 0.125931i −0.900087 0.435711i \(-0.856497\pi\)
0.827380 + 0.561642i \(0.189830\pi\)
\(354\) −0.324129 + 0.561409i −0.0172273 + 0.0298385i
\(355\) −14.3123 24.7896i −0.759618 1.31570i
\(356\) −18.3325 −0.971619
\(357\) −3.41269 4.87648i −0.180619 0.258091i
\(358\) −8.57318 −0.453107
\(359\) −8.33886 14.4433i −0.440108 0.762290i 0.557589 0.830117i \(-0.311727\pi\)
−0.997697 + 0.0678274i \(0.978393\pi\)
\(360\) 5.27840 9.14246i 0.278196 0.481850i
\(361\) 3.15779 5.46945i 0.166199 0.287866i
\(362\) 7.13959 + 12.3661i 0.375248 + 0.649949i
\(363\) −18.9333 −0.993740
\(364\) −6.93269 + 14.8572i −0.363372 + 0.778731i
\(365\) −21.4486 −1.12267
\(366\) −3.46449 6.00067i −0.181092 0.313660i
\(367\) 14.0388 24.3158i 0.732817 1.26928i −0.222857 0.974851i \(-0.571538\pi\)
0.955674 0.294425i \(-0.0951283\pi\)
\(368\) −0.400435 + 0.693574i −0.0208741 + 0.0361551i
\(369\) 1.98904 + 3.44511i 0.103545 + 0.179345i
\(370\) −12.1580 −0.632066
\(371\) 14.1370 30.2965i 0.733955 1.57292i
\(372\) −14.8586 −0.770383
\(373\) −11.1699 19.3468i −0.578356 1.00174i −0.995668 0.0929784i \(-0.970361\pi\)
0.417312 0.908763i \(-0.362972\pi\)
\(374\) −4.73304 + 8.19786i −0.244740 + 0.423901i
\(375\) −12.5191 + 21.6838i −0.646486 + 1.11975i
\(376\) 0.679413 + 1.17678i 0.0350381 + 0.0606877i
\(377\) 20.7193 1.06710
\(378\) −1.16670 1.66713i −0.0600085 0.0857478i
\(379\) 27.7949 1.42773 0.713864 0.700284i \(-0.246943\pi\)
0.713864 + 0.700284i \(0.246943\pi\)
\(380\) −10.1007 17.4950i −0.518157 0.897475i
\(381\) −0.0473538 + 0.0820192i −0.00242601 + 0.00420197i
\(382\) −8.82096 + 15.2783i −0.451319 + 0.781708i
\(383\) −3.29578 5.70845i −0.168406 0.291688i 0.769453 0.638703i \(-0.220529\pi\)
−0.937860 + 0.347015i \(0.887195\pi\)
\(384\) −9.48405 −0.483981
\(385\) −58.0727 + 5.06569i −2.95966 + 0.258172i
\(386\) 7.79052 0.396527
\(387\) −1.30544 2.26108i −0.0663591 0.114937i
\(388\) −4.47632 + 7.75321i −0.227250 + 0.393609i
\(389\) −4.49456 + 7.78481i −0.227883 + 0.394706i −0.957181 0.289491i \(-0.906514\pi\)
0.729297 + 0.684197i \(0.239847\pi\)
\(390\) −6.81315 11.8007i −0.344997 0.597553i
\(391\) −2.24965 −0.113770
\(392\) 18.0730 3.17720i 0.912823 0.160473i
\(393\) 13.7260 0.692387
\(394\) −1.73648 3.00767i −0.0874827 0.151524i
\(395\) −27.0689 + 46.8848i −1.36199 + 2.35903i
\(396\) 3.85304 6.67367i 0.193623 0.335364i
\(397\) 1.27586 + 2.20985i 0.0640334 + 0.110909i 0.896265 0.443519i \(-0.146270\pi\)
−0.832231 + 0.554428i \(0.812937\pi\)
\(398\) −16.0029 −0.802155
\(399\) −9.38725 + 0.818852i −0.469950 + 0.0409939i
\(400\) 8.98373 0.449187
\(401\) −18.6811 32.3567i −0.932892 1.61582i −0.778351 0.627829i \(-0.783944\pi\)
−0.154540 0.987986i \(-0.549390\pi\)
\(402\) 0.538242 0.932263i 0.0268451 0.0464970i
\(403\) −23.2060 + 40.1940i −1.15597 + 2.00220i
\(404\) 1.99716 + 3.45918i 0.0993625 + 0.172101i
\(405\) −4.02709 −0.200108
\(406\) −5.49447 7.85120i −0.272686 0.389648i
\(407\) −21.4769 −1.06457
\(408\) −2.94867 5.10724i −0.145981 0.252846i
\(409\) 5.38652 9.32973i 0.266346 0.461326i −0.701569 0.712601i \(-0.747517\pi\)
0.967916 + 0.251276i \(0.0808501\pi\)
\(410\) 6.16044 10.6702i 0.304242 0.526963i
\(411\) −0.515909 0.893580i −0.0254479 0.0440771i
\(412\) −14.9151 −0.734816
\(413\) −0.942990 + 2.02089i −0.0464015 + 0.0994417i
\(414\) −0.769091 −0.0377987
\(415\) 6.84028 + 11.8477i 0.335776 + 0.581581i
\(416\) −12.8881 + 22.3229i −0.631893 + 1.09447i
\(417\) 0.140936 0.244109i 0.00690168 0.0119541i
\(418\) 7.49308 + 12.9784i 0.366498 + 0.634794i
\(419\) 19.8186 0.968200 0.484100 0.875013i \(-0.339147\pi\)
0.484100 + 0.875013i \(0.339147\pi\)
\(420\) 6.34577 13.5994i 0.309642 0.663585i
\(421\) 3.68979 0.179830 0.0899148 0.995949i \(-0.471341\pi\)
0.0899148 + 0.995949i \(0.471341\pi\)
\(422\) 10.0872 + 17.4715i 0.491037 + 0.850501i
\(423\) 0.259175 0.448904i 0.0126015 0.0218265i
\(424\) 16.5627 28.6874i 0.804356 1.39318i
\(425\) 12.6177 + 21.8545i 0.612048 + 1.06010i
\(426\) −5.46670 −0.264863
\(427\) −13.6670 19.5291i −0.661392 0.945082i
\(428\) 26.5559 1.28363
\(429\) −12.0353 20.8457i −0.581069 1.00644i
\(430\) −4.04320 + 7.00302i −0.194980 + 0.337716i
\(431\) −4.59503 + 7.95882i −0.221335 + 0.383363i −0.955213 0.295918i \(-0.904375\pi\)
0.733879 + 0.679280i \(0.237708\pi\)
\(432\) 0.400435 + 0.693574i 0.0192659 + 0.0333696i
\(433\) 33.6161 1.61549 0.807743 0.589535i \(-0.200689\pi\)
0.807743 + 0.589535i \(0.200689\pi\)
\(434\) 21.3846 1.86539i 1.02650 0.0895415i
\(435\) −18.9652 −0.909313
\(436\) 7.84143 + 13.5818i 0.375536 + 0.650448i
\(437\) −1.78076 + 3.08437i −0.0851853 + 0.147545i
\(438\) −2.04812 + 3.54744i −0.0978628 + 0.169503i
\(439\) 1.15356 + 1.99803i 0.0550565 + 0.0953606i 0.892240 0.451561i \(-0.149133\pi\)
−0.837184 + 0.546922i \(0.815799\pi\)
\(440\) −57.7576 −2.75349
\(441\) −4.49676 5.36462i −0.214132 0.255458i
\(442\) −7.61205 −0.362068
\(443\) 5.69780 + 9.86889i 0.270711 + 0.468885i 0.969044 0.246888i \(-0.0794079\pi\)
−0.698333 + 0.715773i \(0.746075\pi\)
\(444\) 2.76453 4.78830i 0.131199 0.227243i
\(445\) 26.2075 45.3928i 1.24236 2.15182i
\(446\) −0.462903 0.801771i −0.0219191 0.0379650i
\(447\) 5.70250 0.269719
\(448\) 7.65481 0.667731i 0.361656 0.0315473i
\(449\) 3.16307 0.149275 0.0746373 0.997211i \(-0.476220\pi\)
0.0746373 + 0.997211i \(0.476220\pi\)
\(450\) 4.31362 + 7.47141i 0.203346 + 0.352206i
\(451\) 10.8823 18.8487i 0.512426 0.887549i
\(452\) −0.915378 + 1.58548i −0.0430557 + 0.0745747i
\(453\) 1.43814 + 2.49093i 0.0675698 + 0.117034i
\(454\) −10.9620 −0.514470
\(455\) −26.8770 38.4054i −1.26002 1.80047i
\(456\) −9.33633 −0.437214
\(457\) −5.45681 9.45147i −0.255259 0.442121i 0.709707 0.704497i \(-0.248827\pi\)
−0.964966 + 0.262376i \(0.915494\pi\)
\(458\) 4.75185 8.23045i 0.222040 0.384584i
\(459\) −1.12483 + 1.94826i −0.0525024 + 0.0909368i
\(460\) −2.83608 4.91223i −0.132233 0.229034i
\(461\) 34.5807 1.61058 0.805291 0.592880i \(-0.202009\pi\)
0.805291 + 0.592880i \(0.202009\pi\)
\(462\) −4.70751 + 10.0885i −0.219013 + 0.469361i
\(463\) −1.07364 −0.0498961 −0.0249480 0.999689i \(-0.507942\pi\)
−0.0249480 + 0.999689i \(0.507942\pi\)
\(464\) 1.88581 + 3.26633i 0.0875468 + 0.151635i
\(465\) 21.2414 36.7912i 0.985046 1.70615i
\(466\) 4.60791 7.98114i 0.213457 0.369719i
\(467\) 6.74418 + 11.6813i 0.312083 + 0.540544i 0.978813 0.204755i \(-0.0656399\pi\)
−0.666730 + 0.745299i \(0.732307\pi\)
\(468\) 6.19677 0.286446
\(469\) 1.56591 3.35585i 0.0723069 0.154959i
\(470\) −1.60543 −0.0740531
\(471\) 8.37042 + 14.4980i 0.385688 + 0.668032i
\(472\) −1.10479 + 1.91356i −0.0508523 + 0.0880788i
\(473\) −7.14222 + 12.3707i −0.328400 + 0.568805i
\(474\) 5.16960 + 8.95402i 0.237448 + 0.411272i
\(475\) 39.9512 1.83309
\(476\) −4.80677 6.86852i −0.220318 0.314818i
\(477\) −12.6363 −0.578577
\(478\) 2.51467 + 4.35554i 0.115018 + 0.199218i
\(479\) 3.15470 5.46409i 0.144142 0.249661i −0.784911 0.619609i \(-0.787291\pi\)
0.929052 + 0.369948i \(0.120625\pi\)
\(480\) 11.7970 20.4330i 0.538458 0.932637i
\(481\) −8.63521 14.9566i −0.393732 0.681963i
\(482\) −0.384595 −0.0175178
\(483\) −2.63574 + 0.229917i −0.119930 + 0.0104616i
\(484\) −26.6675 −1.21216
\(485\) −12.7984 22.1675i −0.581145 1.00657i
\(486\) −0.384545 + 0.666052i −0.0174433 + 0.0302127i
\(487\) 9.29842 16.1053i 0.421352 0.729803i −0.574720 0.818350i \(-0.694889\pi\)
0.996072 + 0.0885474i \(0.0282225\pi\)
\(488\) −11.8087 20.4533i −0.534555 0.925877i
\(489\) 0.687374 0.0310841
\(490\) −7.42558 + 20.3691i −0.335453 + 0.920182i
\(491\) −27.5620 −1.24386 −0.621928 0.783074i \(-0.713651\pi\)
−0.621928 + 0.783074i \(0.713651\pi\)
\(492\) 2.80156 + 4.85244i 0.126304 + 0.218765i
\(493\) −5.29727 + 9.17514i −0.238577 + 0.413227i
\(494\) −6.02548 + 10.4364i −0.271099 + 0.469558i
\(495\) 11.0164 + 19.0809i 0.495149 + 0.857624i
\(496\) −8.44858 −0.379352
\(497\) −18.7349 + 1.63425i −0.840374 + 0.0733061i
\(498\) 2.61270 0.117078
\(499\) 4.66878 + 8.08657i 0.209004 + 0.362005i 0.951401 0.307955i \(-0.0996447\pi\)
−0.742397 + 0.669960i \(0.766311\pi\)
\(500\) −17.6332 + 30.5416i −0.788581 + 1.36586i
\(501\) −6.20112 + 10.7407i −0.277046 + 0.479857i
\(502\) 1.96147 + 3.39737i 0.0875448 + 0.151632i
\(503\) 32.9700 1.47006 0.735029 0.678035i \(-0.237168\pi\)
0.735029 + 0.678035i \(0.237168\pi\)
\(504\) −3.97669 5.68241i −0.177136 0.253114i
\(505\) −11.4203 −0.508197
\(506\) 2.10390 + 3.64406i 0.0935297 + 0.161998i
\(507\) 3.17805 5.50454i 0.141142 0.244465i
\(508\) −0.0666978 + 0.115524i −0.00295924 + 0.00512555i
\(509\) −11.0073 19.0653i −0.487892 0.845053i 0.512011 0.858979i \(-0.328901\pi\)
−0.999903 + 0.0139256i \(0.995567\pi\)
\(510\) 6.96762 0.308531
\(511\) −5.95859 + 12.7697i −0.263592 + 0.564897i
\(512\) −8.89104 −0.392932
\(513\) 1.78076 + 3.08437i 0.0786225 + 0.136178i
\(514\) −3.40685 + 5.90083i −0.150270 + 0.260275i
\(515\) 21.3222 36.9311i 0.939568 1.62738i
\(516\) −1.83871 3.18473i −0.0809446 0.140200i
\(517\) −2.83596 −0.124725
\(518\) −3.37760 + 7.23843i −0.148403 + 0.318038i
\(519\) 3.20701 0.140772
\(520\) −23.2226 40.2227i −1.01838 1.76388i
\(521\) 9.09504 15.7531i 0.398461 0.690155i −0.595075 0.803670i \(-0.702878\pi\)
0.993536 + 0.113515i \(0.0362110\pi\)
\(522\) −1.81098 + 3.13671i −0.0792646 + 0.137290i
\(523\) −19.5821 33.9172i −0.856265 1.48309i −0.875467 0.483278i \(-0.839446\pi\)
0.0192022 0.999816i \(-0.493887\pi\)
\(524\) 19.3331 0.844572
\(525\) 17.0167 + 24.3157i 0.742671 + 1.06122i
\(526\) −20.1200 −0.877276
\(527\) −11.8661 20.5526i −0.516894 0.895287i
\(528\) 2.19083 3.79464i 0.0953438 0.165140i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) 19.5686 + 33.8938i 0.850005 + 1.47225i
\(531\) 0.842890 0.0365783
\(532\) −13.2219 + 1.15335i −0.573244 + 0.0500042i
\(533\) 17.5017 0.758085
\(534\) −5.00509 8.66907i −0.216591 0.375147i
\(535\) −37.9635 + 65.7546i −1.64130 + 2.84282i
\(536\) 1.83460 3.17762i 0.0792426 0.137252i
\(537\) 5.57358 + 9.65373i 0.240518 + 0.416589i
\(538\) 12.1185 0.522464
\(539\) −13.1171 + 35.9816i −0.564994 + 1.54984i
\(540\) −5.67216 −0.244091
\(541\) −6.20655 10.7501i −0.266841 0.462182i 0.701204 0.712961i \(-0.252646\pi\)
−0.968044 + 0.250780i \(0.919313\pi\)
\(542\) −2.28849 + 3.96378i −0.0982991 + 0.170259i
\(543\) 9.28315 16.0789i 0.398378 0.690011i
\(544\) −6.59016 11.4145i −0.282551 0.489393i
\(545\) −44.8394 −1.92071
\(546\) −8.91845 + 0.777959i −0.381674 + 0.0332936i
\(547\) 25.5889 1.09410 0.547052 0.837099i \(-0.315750\pi\)
0.547052 + 0.837099i \(0.315750\pi\)
\(548\) −0.726657 1.25861i −0.0310413 0.0537651i
\(549\) −4.50466 + 7.80230i −0.192254 + 0.332994i
\(550\) 23.6004 40.8771i 1.00632 1.74301i
\(551\) 8.38634 + 14.5256i 0.357270 + 0.618810i
\(552\) −2.62145 −0.111576
\(553\) 20.3935 + 29.1408i 0.867218 + 1.23919i
\(554\) −11.7183 −0.497862
\(555\) 7.90416 + 13.6904i 0.335513 + 0.581125i
\(556\) 0.198509 0.343827i 0.00841865 0.0145815i
\(557\) −13.7923 + 23.8889i −0.584398 + 1.01221i 0.410553 + 0.911837i \(0.365336\pi\)
−0.994950 + 0.100369i \(0.967998\pi\)
\(558\) −4.05666 7.02635i −0.171732 0.297449i
\(559\) −11.4867 −0.485835
\(560\) 3.60819 7.73262i 0.152474 0.326763i
\(561\) 12.3081 0.519650
\(562\) 0.685469 + 1.18727i 0.0289148 + 0.0500818i
\(563\) −12.6669 + 21.9397i −0.533845 + 0.924647i 0.465373 + 0.885115i \(0.345920\pi\)
−0.999218 + 0.0395326i \(0.987413\pi\)
\(564\) 0.365048 0.632282i 0.0153713 0.0266239i
\(565\) −2.61719 4.53310i −0.110106 0.190709i
\(566\) 15.3811 0.646517
\(567\) −1.11876 + 2.39758i −0.0469834 + 0.100689i
\(568\) −18.6333 −0.781834
\(569\) 11.1027 + 19.2305i 0.465450 + 0.806183i 0.999222 0.0394454i \(-0.0125591\pi\)
−0.533772 + 0.845629i \(0.679226\pi\)
\(570\) 5.51537 9.55289i 0.231013 0.400127i
\(571\) −4.33227 + 7.50371i −0.181300 + 0.314020i −0.942323 0.334704i \(-0.891364\pi\)
0.761024 + 0.648724i \(0.224697\pi\)
\(572\) −16.9517 29.3612i −0.708786 1.22765i
\(573\) 22.9387 0.958277
\(574\) −4.64121 6.63195i −0.193720 0.276812i
\(575\) 11.2175 0.467800
\(576\) −1.45212 2.51514i −0.0605048 0.104797i
\(577\) −20.2143 + 35.0122i −0.841532 + 1.45758i 0.0470678 + 0.998892i \(0.485012\pi\)
−0.888599 + 0.458684i \(0.848321\pi\)
\(578\) −4.59111 + 7.95204i −0.190965 + 0.330761i
\(579\) −5.06476 8.77242i −0.210484 0.364569i
\(580\) −26.7125 −1.10918
\(581\) 8.95396 0.781056i 0.371473 0.0324037i
\(582\) −4.88845 −0.202633
\(583\) 34.5675 + 59.8726i 1.43164 + 2.47967i
\(584\) −6.98101 + 12.0915i −0.288876 + 0.500348i
\(585\) −8.85871 + 15.3437i −0.366262 + 0.634385i
\(586\) −6.70335 11.6105i −0.276913 0.479627i
\(587\) −46.9106 −1.93621 −0.968104 0.250547i \(-0.919389\pi\)
−0.968104 + 0.250547i \(0.919389\pi\)
\(588\) −6.33369 7.55606i −0.261197 0.311607i
\(589\) −37.5714 −1.54810
\(590\) −1.30530 2.26084i −0.0537383 0.0930774i
\(591\) −2.25784 + 3.91069i −0.0928750 + 0.160864i
\(592\) 1.57191 2.72262i 0.0646049 0.111899i
\(593\) −2.84222 4.92286i −0.116716 0.202158i 0.801749 0.597662i \(-0.203903\pi\)
−0.918464 + 0.395504i \(0.870570\pi\)
\(594\) 4.20780 0.172648
\(595\) 23.8786 2.08294i 0.978929 0.0853922i
\(596\) 8.03197 0.329002
\(597\) 10.4038 + 18.0199i 0.425799 + 0.737506i
\(598\) −1.69183 + 2.93033i −0.0691840 + 0.119830i
\(599\) −2.40028 + 4.15741i −0.0980730 + 0.169867i −0.910887 0.412656i \(-0.864601\pi\)
0.812814 + 0.582523i \(0.197935\pi\)
\(600\) 14.7030 + 25.4663i 0.600247 + 1.03966i
\(601\) 8.92677 0.364131 0.182065 0.983286i \(-0.441722\pi\)
0.182065 + 0.983286i \(0.441722\pi\)
\(602\) 3.04610 + 4.35266i 0.124150 + 0.177401i
\(603\) −1.39968 −0.0569996
\(604\) 2.02562 + 3.50848i 0.0824214 + 0.142758i
\(605\) 38.1231 66.0311i 1.54992 2.68454i
\(606\) −1.09052 + 1.88884i −0.0442994 + 0.0767288i
\(607\) −1.66241 2.87939i −0.0674753 0.116871i 0.830314 0.557296i \(-0.188161\pi\)
−0.897789 + 0.440425i \(0.854828\pi\)
\(608\) −20.8663 −0.846242
\(609\) −5.26869 + 11.2912i −0.213498 + 0.457542i
\(610\) 27.9036 1.12978
\(611\) −1.14026 1.97498i −0.0461298 0.0798991i
\(612\) −1.58432 + 2.74412i −0.0640422 + 0.110924i
\(613\) −12.8126 + 22.1921i −0.517497 + 0.896330i 0.482297 + 0.876008i \(0.339803\pi\)
−0.999793 + 0.0203225i \(0.993531\pi\)
\(614\) −8.51409 14.7468i −0.343601 0.595134i
\(615\) −16.0201 −0.645991
\(616\) −16.0455 + 34.3867i −0.646493 + 1.38548i
\(617\) 29.3425 1.18128 0.590642 0.806934i \(-0.298875\pi\)
0.590642 + 0.806934i \(0.298875\pi\)
\(618\) −4.07209 7.05308i −0.163804 0.283716i
\(619\) −2.99870 + 5.19390i −0.120528 + 0.208760i −0.919976 0.391975i \(-0.871792\pi\)
0.799448 + 0.600735i \(0.205125\pi\)
\(620\) 29.9185 51.8203i 1.20156 2.08116i
\(621\) 0.500000 + 0.866025i 0.0200643 + 0.0347524i
\(622\) 5.29930 0.212483
\(623\) −19.7445 28.2134i −0.791046 1.13035i
\(624\) 3.52347 0.141052
\(625\) −22.3721 38.7496i −0.894883 1.54998i
\(626\) 5.21977 9.04091i 0.208624 0.361347i
\(627\) 9.74278 16.8750i 0.389089 0.673922i
\(628\) 11.7897 + 20.4204i 0.470461 + 0.814863i
\(629\) 8.83099 0.352115
\(630\) 8.16342 0.712097i 0.325238 0.0283706i
\(631\) 16.3993 0.652846 0.326423 0.945224i \(-0.394157\pi\)
0.326423 + 0.945224i \(0.394157\pi\)
\(632\) 17.6206 + 30.5198i 0.700909 + 1.21401i
\(633\) 13.1157 22.7171i 0.521304 0.902925i
\(634\) −9.48240 + 16.4240i −0.376594 + 0.652280i
\(635\) −0.190698 0.330299i −0.00756762 0.0131075i
\(636\) −17.7982 −0.705746
\(637\) −30.3318 + 5.33227i −1.20179 + 0.211272i
\(638\) 19.8163 0.784533
\(639\) 3.55400 + 6.15572i 0.140594 + 0.243516i
\(640\) 19.0966 33.0762i 0.754858 1.30745i
\(641\) 24.2326 41.9721i 0.957130 1.65780i 0.227714 0.973728i \(-0.426875\pi\)
0.729416 0.684070i \(-0.239792\pi\)
\(642\) 7.25023 + 12.5578i 0.286144 + 0.495615i
\(643\) −19.8571 −0.783088 −0.391544 0.920159i \(-0.628059\pi\)
−0.391544 + 0.920159i \(0.628059\pi\)
\(644\) −3.71244 + 0.323837i −0.146291 + 0.0127610i
\(645\) 10.5142 0.413997
\(646\) −3.08105 5.33653i −0.121222 0.209963i
\(647\) 14.7065 25.4724i 0.578172 1.00142i −0.417517 0.908669i \(-0.637100\pi\)
0.995689 0.0927538i \(-0.0295670\pi\)
\(648\) −1.31072 + 2.27024i −0.0514900 + 0.0891834i
\(649\) −2.30578 3.99373i −0.0905098 0.156768i
\(650\) 37.9560 1.48876
\(651\) −16.0031 22.8672i −0.627209 0.896236i
\(652\) 0.968166 0.0379163
\(653\) −11.5894 20.0734i −0.453528 0.785534i 0.545074 0.838388i \(-0.316502\pi\)
−0.998602 + 0.0528537i \(0.983168\pi\)
\(654\) −4.28170 + 7.41612i −0.167428 + 0.289993i
\(655\) −27.6380 + 47.8704i −1.07991 + 1.87045i
\(656\) 1.59296 + 2.75909i 0.0621946 + 0.107724i
\(657\) 5.32607 0.207790
\(658\) −0.446002 + 0.955814i −0.0173870 + 0.0372615i
\(659\) 33.1492 1.29131 0.645654 0.763630i \(-0.276585\pi\)
0.645654 + 0.763630i \(0.276585\pi\)
\(660\) 15.5166 + 26.8755i 0.603981 + 1.04613i
\(661\) −7.52823 + 13.0393i −0.292814 + 0.507169i −0.974474 0.224500i \(-0.927925\pi\)
0.681660 + 0.731669i \(0.261258\pi\)
\(662\) 8.83208 15.2976i 0.343269 0.594559i
\(663\) 4.94873 + 8.57146i 0.192193 + 0.332888i
\(664\) 8.90539 0.345596
\(665\) 16.0459 34.3874i 0.622232 1.33349i
\(666\) 3.01906 0.116986
\(667\) 2.35471 + 4.07847i 0.0911746 + 0.157919i
\(668\) −8.73428 + 15.1282i −0.337939 + 0.585328i
\(669\) −0.601883 + 1.04249i −0.0232701 + 0.0403051i
\(670\) 2.16755 + 3.75431i 0.0837398 + 0.145042i
\(671\) 49.2912 1.90286
\(672\) −8.88776 12.7000i −0.342853 0.489912i
\(673\) −23.8903 −0.920904 −0.460452 0.887684i \(-0.652313\pi\)
−0.460452 + 0.887684i \(0.652313\pi\)
\(674\) −7.66160 13.2703i −0.295114 0.511152i
\(675\) 5.60873 9.71461i 0.215880 0.373915i
\(676\) 4.47628 7.75314i 0.172164 0.298198i
\(677\) 4.29280 + 7.43534i 0.164986 + 0.285763i 0.936650 0.350266i \(-0.113909\pi\)
−0.771665 + 0.636030i \(0.780576\pi\)
\(678\) −0.999657 −0.0383916
\(679\) −16.7532 + 1.46138i −0.642927 + 0.0560827i
\(680\) 23.7491 0.910737
\(681\) 7.12657 + 12.3436i 0.273091 + 0.473007i
\(682\) −22.1945 + 38.4421i −0.849873 + 1.47202i
\(683\) 4.69158 8.12606i 0.179518 0.310935i −0.762197 0.647345i \(-0.775879\pi\)
0.941716 + 0.336410i \(0.109213\pi\)
\(684\) 2.50820 + 4.34433i 0.0959034 + 0.166110i
\(685\) 4.15522 0.158763
\(686\) 10.0641 + 10.0796i 0.384249 + 0.384841i
\(687\) −12.3571 −0.471452
\(688\) −1.04549 1.81083i −0.0398588 0.0690374i
\(689\) −27.7971 + 48.1460i −1.05898 + 1.83421i
\(690\) 1.54860 2.68225i 0.0589542 0.102112i
\(691\) 10.6397 + 18.4284i 0.404751 + 0.701050i 0.994293 0.106688i \(-0.0340247\pi\)
−0.589541 + 0.807738i \(0.700691\pi\)
\(692\) 4.51707 0.171713
\(693\) 14.4205 1.25790i 0.547789 0.0477838i
\(694\) −9.71474 −0.368767
\(695\) 0.567564 + 0.983049i 0.0215289 + 0.0372892i
\(696\) −6.17273 + 10.6915i −0.233977 + 0.405260i
\(697\) −4.47464 + 7.75030i −0.169489 + 0.293563i
\(698\) 5.75651 + 9.97058i 0.217887 + 0.377392i
\(699\) −11.9828 −0.453230
\(700\) 23.9680 + 34.2486i 0.905907 + 1.29448i
\(701\) −4.27651 −0.161521 −0.0807607 0.996734i \(-0.525735\pi\)
−0.0807607 + 0.996734i \(0.525735\pi\)
\(702\) 1.69183 + 2.93033i 0.0638540 + 0.110598i
\(703\) 6.99036 12.1077i 0.263646 0.456649i
\(704\) −7.94472 + 13.7607i −0.299428 + 0.518624i
\(705\) 1.04372 + 1.80778i 0.0393088 + 0.0680849i
\(706\) −2.10120 −0.0790797
\(707\) −3.17265 + 6.79922i −0.119320 + 0.255711i
\(708\) 1.18721 0.0446181
\(709\) 6.86581 + 11.8919i 0.257851 + 0.446611i 0.965666 0.259787i \(-0.0836523\pi\)
−0.707815 + 0.706398i \(0.750319\pi\)
\(710\) 11.0075 19.0655i 0.413102 0.715514i
\(711\) 6.72171 11.6423i 0.252084 0.436622i
\(712\) −17.0599 29.5485i −0.639345 1.10738i
\(713\) −10.5492 −0.395072
\(714\) 1.93566 4.14826i 0.0724402 0.155245i
\(715\) 96.9343 3.62514
\(716\) 7.85039 + 13.5973i 0.293383 + 0.508154i
\(717\) 3.26967 5.66324i 0.122108 0.211497i
\(718\) 6.41334 11.1082i 0.239344 0.414556i
\(719\) −8.84409 15.3184i −0.329829 0.571280i 0.652649 0.757660i \(-0.273658\pi\)
−0.982478 + 0.186380i \(0.940324\pi\)
\(720\) −3.22518 −0.120195
\(721\) −16.0639 22.9542i −0.598252 0.854859i
\(722\) 4.85725 0.180768
\(723\) 0.250032 + 0.433069i 0.00929880 + 0.0161060i
\(724\) 13.0753 22.6471i 0.485940 0.841673i
\(725\) 26.4138 45.7501i 0.980985 1.69912i
\(726\) −7.28071 12.6106i −0.270213 0.468022i
\(727\) 25.0455 0.928885 0.464442 0.885603i \(-0.346255\pi\)
0.464442 + 0.885603i \(0.346255\pi\)
\(728\) −30.3985 + 2.65167i −1.12664 + 0.0982775i
\(729\) 1.00000 0.0370370
\(730\) −8.24795 14.2859i −0.305270 0.528744i
\(731\) 2.93678 5.08665i 0.108621 0.188137i
\(732\) −6.34481 + 10.9895i −0.234511 + 0.406185i
\(733\) −7.89251 13.6702i −0.291517 0.504922i 0.682652 0.730744i \(-0.260827\pi\)
−0.974169 + 0.225822i \(0.927493\pi\)
\(734\) 21.5942 0.797055
\(735\) 27.7639 4.88084i 1.02409 0.180033i
\(736\) −5.85883 −0.215959
\(737\) 3.82893 + 6.63190i 0.141040 + 0.244289i
\(738\) −1.52975 + 2.64960i −0.0563108 + 0.0975332i
\(739\) 4.99929 8.65903i 0.183902 0.318528i −0.759304 0.650736i \(-0.774460\pi\)
0.943206 + 0.332209i \(0.107794\pi\)
\(740\) 11.1330 + 19.2829i 0.409257 + 0.708854i
\(741\) 15.6691 0.575619
\(742\) 25.6154 2.23444i 0.940370 0.0820288i
\(743\) −7.14322 −0.262059 −0.131030 0.991378i \(-0.541828\pi\)
−0.131030 + 0.991378i \(0.541828\pi\)
\(744\) −13.8271 23.9493i −0.506927 0.878024i
\(745\) −11.4822 + 19.8878i −0.420677 + 0.728634i
\(746\) 8.59067 14.8795i 0.314527 0.544776i
\(747\) −1.69857 2.94200i −0.0621472 0.107642i
\(748\) 17.3360 0.633867
\(749\) 28.6013 + 40.8692i 1.04507 + 1.49333i
\(750\) −19.2567 −0.703156
\(751\) 10.6810 + 18.5000i 0.389754 + 0.675073i 0.992416 0.122923i \(-0.0392268\pi\)
−0.602663 + 0.797996i \(0.705893\pi\)
\(752\) 0.207566 0.359514i 0.00756914 0.0131101i
\(753\) 2.55038 4.41738i 0.0929409 0.160978i
\(754\) 7.96752 + 13.8001i 0.290160 + 0.502572i
\(755\) −11.5831 −0.421550
\(756\) −1.57577 + 3.37699i −0.0573102 + 0.122820i
\(757\) −6.60015 −0.239887 −0.119943 0.992781i \(-0.538271\pi\)
−0.119943 + 0.992781i \(0.538271\pi\)
\(758\) 10.6884 + 18.5129i 0.388220 + 0.672417i
\(759\) 2.73557 4.73814i 0.0992948 0.171984i
\(760\) 18.7991 32.5610i 0.681916 1.18111i
\(761\) −6.57699 11.3917i −0.238416 0.412948i 0.721844 0.692056i \(-0.243295\pi\)
−0.960260 + 0.279108i \(0.909961\pi\)
\(762\) −0.0728387 −0.00263867
\(763\) −12.4567 + 26.6957i −0.450964 + 0.966449i
\(764\) 32.3091 1.16890
\(765\) −4.52978 7.84580i −0.163774 0.283666i
\(766\) 2.53475 4.39032i 0.0915843 0.158629i
\(767\) 1.85417 3.21152i 0.0669502 0.115961i
\(768\) −6.55128 11.3471i −0.236399 0.409455i
\(769\) −23.8184 −0.858915 −0.429457 0.903087i \(-0.641295\pi\)
−0.429457 + 0.903087i \(0.641295\pi\)
\(770\) −25.7056 36.7314i −0.926365 1.32371i
\(771\) 8.85942 0.319064
\(772\) −7.13371 12.3560i −0.256748 0.444700i
\(773\) 0.897935 1.55527i 0.0322965 0.0559391i −0.849425 0.527709i \(-0.823051\pi\)
0.881722 + 0.471770i \(0.156385\pi\)
\(774\) 1.00400 1.73898i 0.0360880 0.0625063i
\(775\) 59.1679 + 102.482i 2.12537 + 3.68126i
\(776\) −16.6623 −0.598141
\(777\) 10.3466 0.902536i 0.371182 0.0323783i
\(778\) −6.91345 −0.247859
\(779\) 7.08399 + 12.2698i 0.253810 + 0.439612i
\(780\) −12.4775 + 21.6116i −0.446766 + 0.773821i
\(781\) 19.4444 33.6787i 0.695776 1.20512i
\(782\) −0.865093 1.49838i −0.0309357 0.0535821i
\(783\) 4.70941 0.168301
\(784\) −3.60132 4.29636i −0.128619 0.153442i
\(785\) −67.4169 −2.40621
\(786\) 5.27829 + 9.14226i 0.188270 + 0.326094i
\(787\) 7.53744 13.0552i 0.268681 0.465369i −0.699841 0.714299i \(-0.746746\pi\)
0.968521 + 0.248930i \(0.0800790\pi\)
\(788\) −3.18016 + 5.50820i −0.113289 + 0.196222i
\(789\) 13.0804 + 22.6559i 0.465675 + 0.806573i
\(790\) −41.6369 −1.48138
\(791\) −3.42591 + 0.298844i −0.121812 + 0.0106257i
\(792\) 14.3423 0.509631
\(793\) 19.8185 + 34.3266i 0.703775 + 1.21897i
\(794\) −0.981249 + 1.69957i −0.0348232 + 0.0603156i
\(795\) 25.4438 44.0699i 0.902398 1.56300i
\(796\) 14.6538 + 25.3811i 0.519389 + 0.899608i
\(797\) 20.9322 0.741456 0.370728 0.928742i \(-0.379108\pi\)
0.370728 + 0.928742i \(0.379108\pi\)
\(798\) −4.15522 5.93751i −0.147093 0.210186i
\(799\) 1.16611 0.0412539
\(800\) 32.8606 + 56.9163i 1.16180 + 2.01229i
\(801\) −6.50780 + 11.2718i −0.229942 + 0.398271i
\(802\) 14.3675 24.8852i 0.507334 0.878728i
\(803\) −14.5698 25.2357i −0.514158 0.890548i
\(804\) −1.97146 −0.0695279
\(805\) 4.50534 9.65527i 0.158792 0.340303i
\(806\) −35.6950 −1.25730
\(807\) −7.87844 13.6459i −0.277334 0.480357i
\(808\) −3.71704 + 6.43810i −0.130765 + 0.226492i
\(809\) −12.4493 + 21.5628i −0.437694 + 0.758108i −0.997511 0.0705081i \(-0.977538\pi\)
0.559817 + 0.828616i \(0.310871\pi\)
\(810\) −1.54860 2.68225i −0.0544122 0.0942447i
\(811\) 33.0135 1.15926 0.579630 0.814880i \(-0.303197\pi\)
0.579630 + 0.814880i \(0.303197\pi\)
\(812\) −7.42095 + 15.9036i −0.260424 + 0.558108i
\(813\) 5.95116 0.208716
\(814\) −8.25884 14.3047i −0.289472 0.501380i
\(815\) −1.38406 + 2.39726i −0.0484815 + 0.0839724i
\(816\) −0.900840 + 1.56030i −0.0315357 + 0.0546214i
\(817\) −4.64934 8.05289i −0.162660 0.281735i
\(818\) 8.28545 0.289694
\(819\) 6.67406 + 9.53675i 0.233211 + 0.333241i
\(820\) −22.5642 −0.787977
\(821\) −3.53329 6.11983i −0.123312 0.213584i 0.797760 0.602976i \(-0.206018\pi\)
−0.921072 + 0.389392i \(0.872685\pi\)
\(822\) 0.396781 0.687244i 0.0138393 0.0239704i
\(823\) −19.1629 + 33.1911i −0.667975 + 1.15697i 0.310494 + 0.950575i \(0.399506\pi\)
−0.978469 + 0.206392i \(0.933828\pi\)
\(824\) −13.8797 24.0404i −0.483523 0.837487i
\(825\) −61.3722 −2.13671
\(826\) −1.70864 + 0.149045i −0.0594513 + 0.00518595i
\(827\) −18.8543 −0.655629 −0.327815 0.944742i \(-0.606312\pi\)
−0.327815 + 0.944742i \(0.606312\pi\)
\(828\) 0.704250 + 1.21980i 0.0244744 + 0.0423909i
\(829\) −24.5960 + 42.6016i −0.854255 + 1.47961i 0.0230794 + 0.999734i \(0.492653\pi\)
−0.877334 + 0.479879i \(0.840680\pi\)
\(830\) −5.26079 + 9.11196i −0.182605 + 0.316281i
\(831\) 7.61827 + 13.1952i 0.264275 + 0.457738i
\(832\) −12.7773 −0.442974
\(833\) 5.39357 14.7951i 0.186876 0.512620i
\(834\) 0.216786 0.00750668
\(835\) −24.9725 43.2536i −0.864208 1.49685i
\(836\) 13.7227 23.7684i 0.474609 0.822047i
\(837\) −5.27462 + 9.13592i −0.182318 + 0.315783i
\(838\) 7.62113 + 13.2002i 0.263268 + 0.455993i
\(839\) 3.42024 0.118080 0.0590399 0.998256i \(-0.481196\pi\)
0.0590399 + 0.998256i \(0.481196\pi\)
\(840\) 27.8250 2.42718i 0.960054 0.0837458i
\(841\) −6.82142 −0.235222
\(842\) 1.41889 + 2.45759i 0.0488983 + 0.0846943i
\(843\) 0.891272 1.54373i 0.0306970 0.0531688i
\(844\) 18.4735 31.9971i 0.635884 1.10138i
\(845\) 12.7983 + 22.1673i 0.440274 + 0.762577i
\(846\) 0.398658 0.0137062
\(847\) −28.7215 41.0410i −0.986883 1.41018i
\(848\) −10.1200 −0.347524
\(849\) −9.99956 17.3197i −0.343184 0.594412i
\(850\) −9.70415 + 16.8081i −0.332849 + 0.576512i
\(851\) 1.96275 3.39958i 0.0672821 0.116536i
\(852\) 5.00581 + 8.67032i 0.171496 + 0.297040i
\(853\) 26.9555 0.922939 0.461469 0.887156i \(-0.347322\pi\)
0.461469 + 0.887156i \(0.347322\pi\)
\(854\) 7.75185 16.6128i 0.265263 0.568477i
\(855\) −14.3426 −0.490505
\(856\) 24.7124 + 42.8031i 0.844653 + 1.46298i
\(857\) −10.5721 + 18.3114i −0.361137 + 0.625507i −0.988148 0.153503i \(-0.950945\pi\)
0.627012 + 0.779010i \(0.284278\pi\)
\(858\) 9.25622 16.0322i 0.316002 0.547332i
\(859\) −20.6665 35.7955i −0.705133 1.22133i −0.966644 0.256125i \(-0.917554\pi\)
0.261511 0.965201i \(-0.415779\pi\)
\(860\) 14.8093 0.504992
\(861\) −4.45050 + 9.53774i −0.151673 + 0.325045i
\(862\) −7.06798 −0.240736
\(863\) 0.688390 + 1.19233i 0.0234331 + 0.0405873i 0.877504 0.479569i \(-0.159207\pi\)
−0.854071 + 0.520156i \(0.825874\pi\)
\(864\) −2.92942 + 5.07390i −0.0996608 + 0.172617i
\(865\) −6.45746 + 11.1846i −0.219560 + 0.380289i
\(866\) 12.9269 + 22.3901i 0.439274 + 0.760845i
\(867\) 11.9391 0.405472
\(868\) −22.5403 32.2084i −0.765067 1.09323i
\(869\) −73.5507 −2.49504
\(870\) −7.29299 12.6318i −0.247256 0.428259i
\(871\) −3.07900 + 5.33298i −0.104328 + 0.180701i
\(872\) −14.5942 + 25.2778i −0.494221 + 0.856015i
\(873\) 3.17807 + 5.50458i 0.107561 + 0.186302i
\(874\) −2.73913 −0.0926525
\(875\) −65.9945 + 5.75672i −2.23102 + 0.194613i
\(876\) 7.50177 0.253461
\(877\) 11.2162 + 19.4271i 0.378745 + 0.656006i 0.990880 0.134748i \(-0.0430224\pi\)
−0.612135 + 0.790753i \(0.709689\pi\)
\(878\) −0.887193 + 1.53666i −0.0299413 + 0.0518599i
\(879\) −8.71595 + 15.0965i −0.293982 + 0.509191i
\(880\) 8.82269 + 15.2813i 0.297413 + 0.515134i
\(881\) −51.4107 −1.73207 −0.866036 0.499982i \(-0.833340\pi\)
−0.866036 + 0.499982i \(0.833340\pi\)
\(882\) 1.84391 5.05802i 0.0620875 0.170312i
\(883\) 47.4947 1.59833 0.799163 0.601115i \(-0.205277\pi\)
0.799163 + 0.601115i \(0.205277\pi\)
\(884\) 6.97029 + 12.0729i 0.234436 + 0.406055i
\(885\) −1.69720 + 2.93963i −0.0570507 + 0.0988146i
\(886\) −4.38213 + 7.59007i −0.147220 + 0.254993i
\(887\) 8.01467 + 13.8818i 0.269106 + 0.466106i 0.968631 0.248502i \(-0.0799384\pi\)
−0.699525 + 0.714608i \(0.746605\pi\)
\(888\) 10.2905 0.345325
\(889\) −0.249625 + 0.0217748i −0.00837215 + 0.000730305i
\(890\) 40.3119 1.35126
\(891\) −2.73557 4.73814i −0.0916449 0.158734i
\(892\) −0.847752 + 1.46835i −0.0283848 + 0.0491640i
\(893\) 0.923057 1.59878i 0.0308889 0.0535012i
\(894\) 2.19287 + 3.79816i 0.0733405 + 0.127030i
\(895\) −44.8906 −1.50053
\(896\) −14.3872 20.5582i −0.480641 0.686801i
\(897\) 4.39956 0.146897
\(898\) 1.21634 + 2.10677i 0.0405899 + 0.0703038i
\(899\) −24.8404 + 43.0248i −0.828473 + 1.43496i
\(900\) 7.89990 13.6830i 0.263330 0.456101i
\(901\) −14.2136 24.6188i −0.473525 0.820170i
\(902\) 16.7389 0.557345
\(903\) 2.92094 6.25977i 0.0972026 0.208312i
\(904\) −3.40733 −0.113326
\(905\) 37.3841 + 64.7512i 1.24269 + 2.15240i
\(906\) −1.10606 + 1.91575i −0.0367464 + 0.0636467i
\(907\) 14.4438 25.0173i 0.479597 0.830686i −0.520129 0.854088i \(-0.674116\pi\)
0.999726 + 0.0234013i \(0.00744954\pi\)
\(908\) 10.0378 + 17.3859i 0.333115 + 0.576973i
\(909\) 2.83587 0.0940599
\(910\) 15.2445 32.6701i 0.505351 1.08300i
\(911\) 41.9126 1.38863 0.694314 0.719672i \(-0.255708\pi\)
0.694314 + 0.719672i \(0.255708\pi\)
\(912\) 1.42616 + 2.47018i 0.0472248 + 0.0817958i
\(913\) −9.29308 + 16.0961i −0.307556 + 0.532702i
\(914\) 4.19678 7.26904i 0.138817 0.240438i
\(915\) −18.1407 31.4206i −0.599712 1.03873i
\(916\) −17.4049 −0.575075
\(917\) 20.8222 + 29.7534i 0.687610 + 0.982544i
\(918\) −1.73019 −0.0571046
\(919\) −2.49499 4.32146i −0.0823023 0.142552i 0.821936 0.569580i \(-0.192894\pi\)
−0.904238 + 0.427028i \(0.859561\pi\)
\(920\) 5.27840 9.14246i 0.174024 0.301418i
\(921\) −11.0703 + 19.1744i −0.364780 + 0.631817i
\(922\) 13.2978 + 23.0325i 0.437941 + 0.758536i
\(923\) 31.2721 1.02933
\(924\) 20.3113 1.77176i 0.668192 0.0582865i
\(925\) −44.0341 −1.44783
\(926\) −0.412862 0.715097i −0.0135675 0.0234996i
\(927\) −5.29469 + 9.17067i −0.173900 + 0.301204i
\(928\) −13.7958 + 23.8951i −0.452870 + 0.784394i
\(929\) 18.4714 + 31.9935i 0.606028 + 1.04967i 0.991888 + 0.127114i \(0.0405715\pi\)
−0.385860 + 0.922557i \(0.626095\pi\)
\(930\) 32.6731 1.07139
\(931\) −16.0153 19.1062i −0.524881 0.626180i
\(932\) −16.8777 −0.552848
\(933\) −3.44517 5.96722i −0.112790 0.195358i
\(934\) −5.18688 + 8.98395i −0.169720 + 0.293964i
\(935\) −24.7830 + 42.9254i −0.810491 + 1.40381i
\(936\) 5.76660 + 9.98804i 0.188487 + 0.326469i
\(937\) −7.79921 −0.254789 −0.127395 0.991852i \(-0.540661\pi\)
−0.127395 + 0.991852i \(0.540661\pi\)
\(938\) 2.83734 0.247502i 0.0926423 0.00808121i
\(939\) −13.5739 −0.442967
\(940\) 1.47008 + 2.54626i 0.0479488 + 0.0830497i
\(941\) 11.6540 20.1854i 0.379910 0.658024i −0.611139 0.791524i \(-0.709288\pi\)
0.991049 + 0.133500i \(0.0426216\pi\)
\(942\) −6.43761 + 11.1503i −0.209749 + 0.363295i
\(943\) 1.98904 + 3.44511i 0.0647719 + 0.112188i
\(944\) 0.675046 0.0219709
\(945\) −6.10904 8.72937i −0.198727 0.283966i
\(946\) −10.9860 −0.357187
\(947\) −18.7793 32.5267i −0.610244 1.05697i −0.991199 0.132381i \(-0.957738\pi\)
0.380954 0.924594i \(-0.375595\pi\)
\(948\) 9.46752 16.3982i 0.307491 0.532590i
\(949\) 11.7162 20.2930i 0.380323 0.658739i
\(950\) 15.3631 + 26.6096i 0.498443 + 0.863329i
\(951\) 24.6587 0.799614
\(952\) 6.59769 14.1393i 0.213832 0.458258i
\(953\) −16.0283 −0.519209 −0.259604 0.965715i \(-0.583592\pi\)
−0.259604 + 0.965715i \(0.583592\pi\)
\(954\) −4.85923 8.41644i −0.157324 0.272492i
\(955\) −46.1881 + 80.0001i −1.49461 + 2.58874i
\(956\) 4.60533 7.97667i 0.148947 0.257984i
\(957\) −12.8829 22.3139i −0.416445 0.721305i
\(958\) 4.85249 0.156777
\(959\) 1.15435 2.47386i 0.0372760 0.0798852i
\(960\) 11.6956 0.377474
\(961\) −40.1433 69.5303i −1.29495 2.24291i
\(962\) 6.64126 11.5030i 0.214123 0.370872i
\(963\) 9.42702 16.3281i 0.303781 0.526165i
\(964\) 0.352170 + 0.609977i 0.0113426 + 0.0196460i
\(965\) 40.7925 1.31316
\(966\) −1.16670 1.66713i −0.0375379 0.0536390i
\(967\) −49.3526 −1.58707 −0.793536 0.608523i \(-0.791762\pi\)
−0.793536 + 0.608523i \(0.791762\pi\)
\(968\) −24.8163 42.9831i −0.797626 1.38153i
\(969\) −4.00609 + 6.93875i −0.128694 + 0.222905i
\(970\) 9.84312 17.0488i 0.316044 0.547404i
\(971\) 7.59831 + 13.1607i 0.243841 + 0.422346i 0.961805 0.273735i \(-0.0882590\pi\)
−0.717964 + 0.696080i \(0.754926\pi\)
\(972\) 1.40850 0.0451776
\(973\) 0.742944 0.0648072i 0.0238177 0.00207762i
\(974\) 14.3027 0.458287
\(975\) −24.6759 42.7400i −0.790262 1.36877i
\(976\) −3.60765 + 6.24863i −0.115478 + 0.200014i
\(977\) 24.1383 41.8088i 0.772253 1.33758i −0.164073 0.986448i \(-0.552463\pi\)
0.936326 0.351133i \(-0.114203\pi\)
\(978\) 0.264327 + 0.457827i 0.00845223 + 0.0146397i
\(979\) 71.2101 2.27589
\(980\) 39.1054 6.87466i 1.24918 0.219603i
\(981\) 11.1344 0.355495
\(982\) −10.5988 18.3577i −0.338223 0.585819i
\(983\) 6.63330 11.4892i 0.211570 0.366449i −0.740636 0.671906i \(-0.765476\pi\)
0.952206 + 0.305457i \(0.0988092\pi\)
\(984\) −5.21415 + 9.03117i −0.166221 + 0.287903i
\(985\) −9.09252 15.7487i −0.289712 0.501795i
\(986\) −8.14816 −0.259490
\(987\) 1.36624 0.119177i 0.0434878 0.00379345i
\(988\) 22.0699 0.702138
\(989\) −1.30544 2.26108i −0.0415105 0.0718983i
\(990\) −8.47259 + 14.6750i −0.269277 + 0.466401i
\(991\) −0.702165 + 1.21618i −0.0223050 + 0.0386334i −0.876962 0.480559i \(-0.840434\pi\)
0.854657 + 0.519192i \(0.173767\pi\)
\(992\) −30.9031 53.5258i −0.981176 1.69945i
\(993\) −22.9676 −0.728855
\(994\) −8.29291 11.8500i −0.263035 0.375858i
\(995\) −83.7942 −2.65645
\(996\) −2.39243 4.14381i −0.0758070 0.131302i
\(997\) −5.03552 + 8.72178i −0.159477 + 0.276221i −0.934680 0.355490i \(-0.884314\pi\)
0.775204 + 0.631712i \(0.217647\pi\)
\(998\) −3.59072 + 6.21931i −0.113662 + 0.196869i
\(999\) −1.96275 3.39958i −0.0620985 0.107558i
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 483.2.i.h.277.7 20
7.2 even 3 inner 483.2.i.h.415.7 yes 20
7.3 odd 6 3381.2.a.bj.1.4 10
7.4 even 3 3381.2.a.bi.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.i.h.277.7 20 1.1 even 1 trivial
483.2.i.h.415.7 yes 20 7.2 even 3 inner
3381.2.a.bi.1.4 10 7.4 even 3
3381.2.a.bj.1.4 10 7.3 odd 6