Properties

Label 315.2.t.c.131.2
Level $315$
Weight $2$
Character 315.131
Analytic conductor $2.515$
Analytic rank $0$
Dimension $32$
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] = [315,2,Mod(101,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.t (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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.2
Character \(\chi\) \(=\) 315.131
Dual form 315.2.t.c.101.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.44435i q^{2} +(0.807396 - 1.53235i) q^{3} -3.97484 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.74561 - 1.97356i) q^{6} +(0.510801 - 2.59597i) q^{7} +4.82720i q^{8} +(-1.69622 - 2.47444i) q^{9} +O(q^{10})\) \(q-2.44435i q^{2} +(0.807396 - 1.53235i) q^{3} -3.97484 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.74561 - 1.97356i) q^{6} +(0.510801 - 2.59597i) q^{7} +4.82720i q^{8} +(-1.69622 - 2.47444i) q^{9} +(-2.11687 + 1.22217i) q^{10} +(3.79537 + 2.19126i) q^{11} +(-3.20927 + 6.09087i) q^{12} +(1.54497 + 0.891986i) q^{13} +(-6.34547 - 1.24858i) q^{14} +(-1.73076 + 0.0669518i) q^{15} +3.84969 q^{16} +(3.92956 + 6.80619i) q^{17} +(-6.04838 + 4.14616i) q^{18} +(-3.33955 - 1.92809i) q^{19} +(1.98742 + 3.44231i) q^{20} +(-3.56554 - 2.87871i) q^{21} +(5.35620 - 9.27721i) q^{22} +(-1.96471 + 1.13433i) q^{23} +(7.39699 + 3.89747i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.18033 - 3.77644i) q^{26} +(-5.16124 + 0.601365i) q^{27} +(-2.03035 + 10.3186i) q^{28} +(0.771716 - 0.445550i) q^{29} +(0.163653 + 4.23057i) q^{30} -7.07941i q^{31} +0.244430i q^{32} +(6.42215 - 4.04664i) q^{33} +(16.6367 - 9.60521i) q^{34} +(-2.50358 + 0.855621i) q^{35} +(6.74222 + 9.83549i) q^{36} +(2.58988 - 4.48580i) q^{37} +(-4.71293 + 8.16304i) q^{38} +(2.61424 - 1.64725i) q^{39} +(4.18048 - 2.41360i) q^{40} +(1.78706 - 3.09527i) q^{41} +(-7.03657 + 8.71541i) q^{42} +(2.68755 + 4.65498i) q^{43} +(-15.0860 - 8.70991i) q^{44} +(-1.29481 + 2.70619i) q^{45} +(2.77269 + 4.80244i) q^{46} +0.599871 q^{47} +(3.10822 - 5.89909i) q^{48} +(-6.47817 - 2.65205i) q^{49} +(2.11687 + 1.22217i) q^{50} +(13.6022 - 0.526181i) q^{51} +(-6.14099 - 3.54551i) q^{52} +(11.9100 - 6.87623i) q^{53} +(1.46995 + 12.6159i) q^{54} -4.38252i q^{55} +(12.5313 + 2.46574i) q^{56} +(-5.65086 + 3.56065i) q^{57} +(-1.08908 - 1.88634i) q^{58} -8.92852 q^{59} +(6.87948 - 0.266123i) q^{60} +4.34422i q^{61} -17.3045 q^{62} +(-7.29000 + 3.13941i) q^{63} +8.29685 q^{64} -1.78397i q^{65} +(-9.89141 - 15.6980i) q^{66} -6.48717 q^{67} +(-15.6194 - 27.0535i) q^{68} +(0.151890 + 3.92648i) q^{69} +(2.09144 + 6.11962i) q^{70} +0.343987i q^{71} +(11.9446 - 8.18801i) q^{72} +(-3.38926 + 1.95679i) q^{73} +(-10.9649 - 6.33057i) q^{74} +(0.923360 + 1.46540i) q^{75} +(13.2742 + 7.66386i) q^{76} +(7.62713 - 8.73339i) q^{77} +(-4.02645 - 6.39011i) q^{78} +6.87481 q^{79} +(-1.92484 - 3.33393i) q^{80} +(-3.24566 + 8.39439i) q^{81} +(-7.56592 - 4.36819i) q^{82} +(-3.09467 - 5.36013i) q^{83} +(14.1724 + 11.4424i) q^{84} +(3.92956 - 6.80619i) q^{85} +(11.3784 - 6.56931i) q^{86} +(-0.0596608 - 1.54228i) q^{87} +(-10.5777 + 18.3210i) q^{88} +(-1.69019 + 2.92749i) q^{89} +(6.61487 + 3.16497i) q^{90} +(3.10474 - 3.55506i) q^{91} +(7.80941 - 4.50877i) q^{92} +(-10.8482 - 5.71589i) q^{93} -1.46629i q^{94} +3.85618i q^{95} +(0.374553 + 0.197352i) q^{96} +(-10.3098 + 5.95238i) q^{97} +(-6.48254 + 15.8349i) q^{98} +(-1.01567 - 13.1083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44435i 1.72842i −0.503135 0.864208i \(-0.667820\pi\)
0.503135 0.864208i \(-0.332180\pi\)
\(3\) 0.807396 1.53235i 0.466150 0.884705i
\(4\) −3.97484 −1.98742
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −3.74561 1.97356i −1.52914 0.805702i
\(7\) 0.510801 2.59597i 0.193065 0.981186i
\(8\) 4.82720i 1.70667i
\(9\) −1.69622 2.47444i −0.565408 0.824812i
\(10\) −2.11687 + 1.22217i −0.669413 + 0.386486i
\(11\) 3.79537 + 2.19126i 1.14435 + 0.660689i 0.947503 0.319745i \(-0.103597\pi\)
0.196844 + 0.980435i \(0.436931\pi\)
\(12\) −3.20927 + 6.09087i −0.926437 + 1.75828i
\(13\) 1.54497 + 0.891986i 0.428496 + 0.247393i 0.698706 0.715409i \(-0.253760\pi\)
−0.270209 + 0.962802i \(0.587093\pi\)
\(14\) −6.34547 1.24858i −1.69590 0.333696i
\(15\) −1.73076 + 0.0669518i −0.446879 + 0.0172869i
\(16\) 3.84969 0.962422
\(17\) 3.92956 + 6.80619i 0.953058 + 1.65074i 0.738752 + 0.673978i \(0.235416\pi\)
0.214306 + 0.976767i \(0.431251\pi\)
\(18\) −6.04838 + 4.14616i −1.42562 + 0.977259i
\(19\) −3.33955 1.92809i −0.766146 0.442335i 0.0653519 0.997862i \(-0.479183\pi\)
−0.831498 + 0.555528i \(0.812516\pi\)
\(20\) 1.98742 + 3.44231i 0.444401 + 0.769725i
\(21\) −3.56554 2.87871i −0.778064 0.628186i
\(22\) 5.35620 9.27721i 1.14195 1.97791i
\(23\) −1.96471 + 1.13433i −0.409670 + 0.236523i −0.690648 0.723191i \(-0.742675\pi\)
0.280978 + 0.959714i \(0.409341\pi\)
\(24\) 7.39699 + 3.89747i 1.50990 + 0.795567i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.18033 3.77644i 0.427597 0.740620i
\(27\) −5.16124 + 0.601365i −0.993280 + 0.115733i
\(28\) −2.03035 + 10.3186i −0.383701 + 1.95003i
\(29\) 0.771716 0.445550i 0.143304 0.0827366i −0.426634 0.904425i \(-0.640301\pi\)
0.569938 + 0.821688i \(0.306967\pi\)
\(30\) 0.163653 + 4.23057i 0.0298789 + 0.772393i
\(31\) 7.07941i 1.27150i −0.771895 0.635750i \(-0.780691\pi\)
0.771895 0.635750i \(-0.219309\pi\)
\(32\) 0.244430i 0.0432095i
\(33\) 6.42215 4.04664i 1.11795 0.704430i
\(34\) 16.6367 9.60521i 2.85317 1.64728i
\(35\) −2.50358 + 0.855621i −0.423182 + 0.144626i
\(36\) 6.74222 + 9.83549i 1.12370 + 1.63925i
\(37\) 2.58988 4.48580i 0.425774 0.737461i −0.570719 0.821146i \(-0.693335\pi\)
0.996492 + 0.0836841i \(0.0266687\pi\)
\(38\) −4.71293 + 8.16304i −0.764538 + 1.32422i
\(39\) 2.61424 1.64725i 0.418613 0.263771i
\(40\) 4.18048 2.41360i 0.660992 0.381624i
\(41\) 1.78706 3.09527i 0.279091 0.483400i −0.692068 0.721832i \(-0.743300\pi\)
0.971159 + 0.238432i \(0.0766335\pi\)
\(42\) −7.03657 + 8.71541i −1.08577 + 1.34482i
\(43\) 2.68755 + 4.65498i 0.409848 + 0.709877i 0.994872 0.101138i \(-0.0322485\pi\)
−0.585025 + 0.811016i \(0.698915\pi\)
\(44\) −15.0860 8.70991i −2.27430 1.31307i
\(45\) −1.29481 + 2.70619i −0.193019 + 0.403415i
\(46\) 2.77269 + 4.80244i 0.408811 + 0.708081i
\(47\) 0.599871 0.0875002 0.0437501 0.999043i \(-0.486069\pi\)
0.0437501 + 0.999043i \(0.486069\pi\)
\(48\) 3.10822 5.89909i 0.448633 0.851460i
\(49\) −6.47817 2.65205i −0.925452 0.378865i
\(50\) 2.11687 + 1.22217i 0.299370 + 0.172842i
\(51\) 13.6022 0.526181i 1.90469 0.0736801i
\(52\) −6.14099 3.54551i −0.851603 0.491673i
\(53\) 11.9100 6.87623i 1.63596 0.944523i 0.653758 0.756703i \(-0.273191\pi\)
0.982203 0.187820i \(-0.0601421\pi\)
\(54\) 1.46995 + 12.6159i 0.200034 + 1.71680i
\(55\) 4.38252i 0.590939i
\(56\) 12.5313 + 2.46574i 1.67457 + 0.329498i
\(57\) −5.65086 + 3.56065i −0.748475 + 0.471619i
\(58\) −1.08908 1.88634i −0.143003 0.247689i
\(59\) −8.92852 −1.16239 −0.581197 0.813763i \(-0.697416\pi\)
−0.581197 + 0.813763i \(0.697416\pi\)
\(60\) 6.87948 0.266123i 0.888137 0.0343563i
\(61\) 4.34422i 0.556220i 0.960549 + 0.278110i \(0.0897081\pi\)
−0.960549 + 0.278110i \(0.910292\pi\)
\(62\) −17.3045 −2.19768
\(63\) −7.29000 + 3.13941i −0.918454 + 0.395528i
\(64\) 8.29685 1.03711
\(65\) 1.78397i 0.221275i
\(66\) −9.89141 15.6980i −1.21755 1.93229i
\(67\) −6.48717 −0.792534 −0.396267 0.918135i \(-0.629695\pi\)
−0.396267 + 0.918135i \(0.629695\pi\)
\(68\) −15.6194 27.0535i −1.89413 3.28072i
\(69\) 0.151890 + 3.92648i 0.0182854 + 0.472693i
\(70\) 2.09144 + 6.11962i 0.249974 + 0.731435i
\(71\) 0.343987i 0.0408237i 0.999792 + 0.0204119i \(0.00649775\pi\)
−0.999792 + 0.0204119i \(0.993502\pi\)
\(72\) 11.9446 8.18801i 1.40768 0.964967i
\(73\) −3.38926 + 1.95679i −0.396683 + 0.229025i −0.685052 0.728494i \(-0.740220\pi\)
0.288369 + 0.957519i \(0.406887\pi\)
\(74\) −10.9649 6.33057i −1.27464 0.735914i
\(75\) 0.923360 + 1.46540i 0.106620 + 0.169210i
\(76\) 13.2742 + 7.66386i 1.52266 + 0.879105i
\(77\) 7.62713 8.73339i 0.869192 0.995262i
\(78\) −4.02645 6.39011i −0.455906 0.723538i
\(79\) 6.87481 0.773477 0.386739 0.922189i \(-0.373602\pi\)
0.386739 + 0.922189i \(0.373602\pi\)
\(80\) −1.92484 3.33393i −0.215204 0.372744i
\(81\) −3.24566 + 8.39439i −0.360629 + 0.932709i
\(82\) −7.56592 4.36819i −0.835517 0.482386i
\(83\) −3.09467 5.36013i −0.339685 0.588351i 0.644689 0.764445i \(-0.276987\pi\)
−0.984373 + 0.176094i \(0.943654\pi\)
\(84\) 14.1724 + 11.4424i 1.54634 + 1.24847i
\(85\) 3.92956 6.80619i 0.426220 0.738235i
\(86\) 11.3784 6.56931i 1.22696 0.708387i
\(87\) −0.0596608 1.54228i −0.00639631 0.165350i
\(88\) −10.5777 + 18.3210i −1.12758 + 1.95303i
\(89\) −1.69019 + 2.92749i −0.179160 + 0.310313i −0.941593 0.336753i \(-0.890671\pi\)
0.762433 + 0.647067i \(0.224004\pi\)
\(90\) 6.61487 + 3.16497i 0.697269 + 0.333617i
\(91\) 3.10474 3.55506i 0.325466 0.372672i
\(92\) 7.80941 4.50877i 0.814187 0.470071i
\(93\) −10.8482 5.71589i −1.12490 0.592710i
\(94\) 1.46629i 0.151237i
\(95\) 3.85618i 0.395636i
\(96\) 0.374553 + 0.197352i 0.0382277 + 0.0201421i
\(97\) −10.3098 + 5.95238i −1.04680 + 0.604373i −0.921753 0.387777i \(-0.873243\pi\)
−0.125052 + 0.992150i \(0.539910\pi\)
\(98\) −6.48254 + 15.8349i −0.654835 + 1.59957i
\(99\) −1.01567 13.1083i −0.102078 1.31743i
\(100\) 1.98742 3.44231i 0.198742 0.344231i
\(101\) −8.42730 + 14.5965i −0.838547 + 1.45241i 0.0525616 + 0.998618i \(0.483261\pi\)
−0.891109 + 0.453789i \(0.850072\pi\)
\(102\) −1.28617 33.2486i −0.127350 3.29210i
\(103\) 11.5186 6.65028i 1.13496 0.655272i 0.189785 0.981826i \(-0.439221\pi\)
0.945179 + 0.326554i \(0.105887\pi\)
\(104\) −4.30580 + 7.45786i −0.422218 + 0.731304i
\(105\) −0.710267 + 4.52720i −0.0693149 + 0.441809i
\(106\) −16.8079 29.1122i −1.63253 2.82762i
\(107\) 16.8326 + 9.71828i 1.62726 + 0.939502i 0.984905 + 0.173098i \(0.0553779\pi\)
0.642360 + 0.766403i \(0.277955\pi\)
\(108\) 20.5151 2.39033i 1.97407 0.230010i
\(109\) 4.51255 + 7.81596i 0.432224 + 0.748633i 0.997064 0.0765667i \(-0.0243958\pi\)
−0.564841 + 0.825200i \(0.691062\pi\)
\(110\) −10.7124 −1.02139
\(111\) −4.78278 7.59043i −0.453962 0.720452i
\(112\) 1.96642 9.99369i 0.185810 0.944315i
\(113\) 11.4033 + 6.58371i 1.07273 + 0.619343i 0.928927 0.370263i \(-0.120732\pi\)
0.143806 + 0.989606i \(0.454066\pi\)
\(114\) 8.70346 + 13.8127i 0.815154 + 1.29368i
\(115\) 1.96471 + 1.13433i 0.183210 + 0.105776i
\(116\) −3.06745 + 1.77099i −0.284806 + 0.164433i
\(117\) −0.413443 5.33592i −0.0382229 0.493306i
\(118\) 21.8244i 2.00910i
\(119\) 19.6759 6.72442i 1.80369 0.616427i
\(120\) −0.323190 8.35471i −0.0295031 0.762678i
\(121\) 4.10323 + 7.10700i 0.373021 + 0.646091i
\(122\) 10.6188 0.961380
\(123\) −3.30019 5.23751i −0.297568 0.472251i
\(124\) 28.1395i 2.52700i
\(125\) 1.00000 0.0894427
\(126\) 7.67381 + 17.8193i 0.683637 + 1.58747i
\(127\) 3.16484 0.280834 0.140417 0.990092i \(-0.455156\pi\)
0.140417 + 0.990092i \(0.455156\pi\)
\(128\) 19.7915i 1.74934i
\(129\) 9.30299 0.359873i 0.819083 0.0316850i
\(130\) −4.36065 −0.382454
\(131\) −2.94131 5.09450i −0.256984 0.445109i 0.708449 0.705762i \(-0.249395\pi\)
−0.965432 + 0.260653i \(0.916062\pi\)
\(132\) −25.5271 + 16.0848i −2.22184 + 1.40000i
\(133\) −6.71112 + 7.68452i −0.581928 + 0.666333i
\(134\) 15.8569i 1.36983i
\(135\) 3.10142 + 4.16908i 0.266927 + 0.358817i
\(136\) −32.8549 + 18.9688i −2.81728 + 1.62656i
\(137\) 0.431132 + 0.248914i 0.0368341 + 0.0212662i 0.518304 0.855196i \(-0.326564\pi\)
−0.481470 + 0.876463i \(0.659897\pi\)
\(138\) 9.59769 0.371273i 0.817010 0.0316048i
\(139\) −9.77690 5.64470i −0.829266 0.478777i 0.0243354 0.999704i \(-0.492253\pi\)
−0.853601 + 0.520927i \(0.825586\pi\)
\(140\) 9.95134 3.40096i 0.841041 0.287433i
\(141\) 0.484334 0.919216i 0.0407883 0.0774119i
\(142\) 0.840824 0.0705604
\(143\) 3.90915 + 6.77084i 0.326899 + 0.566206i
\(144\) −6.52993 9.52580i −0.544160 0.793817i
\(145\) −0.771716 0.445550i −0.0640875 0.0370009i
\(146\) 4.78308 + 8.28454i 0.395851 + 0.685633i
\(147\) −9.29433 + 7.78559i −0.766583 + 0.642145i
\(148\) −10.2944 + 17.8304i −0.846191 + 1.46565i
\(149\) −9.75448 + 5.63175i −0.799118 + 0.461371i −0.843163 0.537659i \(-0.819309\pi\)
0.0440448 + 0.999030i \(0.485976\pi\)
\(150\) 3.58196 2.25701i 0.292466 0.184284i
\(151\) 1.16713 2.02154i 0.0949800 0.164510i −0.814620 0.579995i \(-0.803055\pi\)
0.909600 + 0.415484i \(0.136388\pi\)
\(152\) 9.30729 16.1207i 0.754921 1.30756i
\(153\) 10.1761 21.2683i 0.822687 1.71944i
\(154\) −21.3475 18.6434i −1.72023 1.50233i
\(155\) −6.13095 + 3.53970i −0.492450 + 0.284316i
\(156\) −10.3912 + 6.54756i −0.831961 + 0.524224i
\(157\) 24.0107i 1.91626i 0.286328 + 0.958132i \(0.407565\pi\)
−0.286328 + 0.958132i \(0.592435\pi\)
\(158\) 16.8044i 1.33689i
\(159\) −0.920752 23.8022i −0.0730204 1.88763i
\(160\) 0.211683 0.122215i 0.0167350 0.00966194i
\(161\) 1.94111 + 5.67975i 0.152981 + 0.447627i
\(162\) 20.5188 + 7.93352i 1.61211 + 0.623316i
\(163\) 6.10651 10.5768i 0.478299 0.828438i −0.521392 0.853318i \(-0.674587\pi\)
0.999690 + 0.0248796i \(0.00792025\pi\)
\(164\) −7.10327 + 12.3032i −0.554672 + 0.960720i
\(165\) −6.71557 3.53843i −0.522807 0.275466i
\(166\) −13.1020 + 7.56447i −1.01692 + 0.587116i
\(167\) −8.16312 + 14.1389i −0.631681 + 1.09410i 0.355527 + 0.934666i \(0.384301\pi\)
−0.987208 + 0.159438i \(0.949032\pi\)
\(168\) 13.8961 17.2116i 1.07211 1.32790i
\(169\) −4.90872 8.50215i −0.377594 0.654012i
\(170\) −16.6367 9.60521i −1.27598 0.736686i
\(171\) 0.893688 + 11.5340i 0.0683420 + 0.882026i
\(172\) −10.6826 18.5028i −0.814540 1.41083i
\(173\) 4.49971 0.342106 0.171053 0.985262i \(-0.445283\pi\)
0.171053 + 0.985262i \(0.445283\pi\)
\(174\) −3.76987 + 0.145832i −0.285793 + 0.0110555i
\(175\) 1.99278 + 1.74035i 0.150640 + 0.131558i
\(176\) 14.6110 + 8.43566i 1.10134 + 0.635862i
\(177\) −7.20886 + 13.6817i −0.541851 + 1.02838i
\(178\) 7.15581 + 4.13141i 0.536351 + 0.309662i
\(179\) 7.40489 4.27521i 0.553467 0.319545i −0.197052 0.980393i \(-0.563137\pi\)
0.750519 + 0.660849i \(0.229803\pi\)
\(180\) 5.14667 10.7567i 0.383610 0.801755i
\(181\) 0.872879i 0.0648806i 0.999474 + 0.0324403i \(0.0103279\pi\)
−0.999474 + 0.0324403i \(0.989672\pi\)
\(182\) −8.68982 7.58908i −0.644132 0.562540i
\(183\) 6.65689 + 3.50751i 0.492091 + 0.259282i
\(184\) −5.47562 9.48405i −0.403668 0.699174i
\(185\) −5.17976 −0.380823
\(186\) −13.9716 + 26.5167i −1.02445 + 1.94430i
\(187\) 34.4427i 2.51870i
\(188\) −2.38439 −0.173900
\(189\) −1.07523 + 13.7056i −0.0782118 + 0.996937i
\(190\) 9.42586 0.683824
\(191\) 15.5264i 1.12345i 0.827324 + 0.561726i \(0.189862\pi\)
−0.827324 + 0.561726i \(0.810138\pi\)
\(192\) 6.69884 12.7137i 0.483447 0.917533i
\(193\) −10.5140 −0.756811 −0.378406 0.925640i \(-0.623528\pi\)
−0.378406 + 0.925640i \(0.623528\pi\)
\(194\) 14.5497 + 25.2008i 1.04461 + 1.80931i
\(195\) −2.73368 1.44037i −0.195763 0.103147i
\(196\) 25.7497 + 10.5415i 1.83926 + 0.752963i
\(197\) 6.18325i 0.440538i 0.975439 + 0.220269i \(0.0706936\pi\)
−0.975439 + 0.220269i \(0.929306\pi\)
\(198\) −32.0412 + 2.48265i −2.27707 + 0.176434i
\(199\) 11.5085 6.64441i 0.815813 0.471010i −0.0331573 0.999450i \(-0.510556\pi\)
0.848971 + 0.528440i \(0.177223\pi\)
\(200\) −4.18048 2.41360i −0.295605 0.170667i
\(201\) −5.23772 + 9.94064i −0.369440 + 0.701159i
\(202\) 35.6790 + 20.5993i 2.51036 + 1.44936i
\(203\) −0.762444 2.23094i −0.0535131 0.156581i
\(204\) −54.0666 + 2.09149i −3.78542 + 0.146433i
\(205\) −3.57411 −0.249627
\(206\) −16.2556 28.1555i −1.13258 1.96169i
\(207\) 6.13940 + 2.93748i 0.426718 + 0.204169i
\(208\) 5.94763 + 3.43387i 0.412394 + 0.238096i
\(209\) −8.44990 14.6357i −0.584492 1.01237i
\(210\) 11.0661 + 1.73614i 0.763630 + 0.119805i
\(211\) 7.79496 13.5013i 0.536627 0.929466i −0.462455 0.886643i \(-0.653031\pi\)
0.999083 0.0428232i \(-0.0136352\pi\)
\(212\) −47.3403 + 27.3319i −3.25135 + 1.87717i
\(213\) 0.527110 + 0.277734i 0.0361170 + 0.0190300i
\(214\) 23.7549 41.1446i 1.62385 2.81259i
\(215\) 2.68755 4.65498i 0.183290 0.317467i
\(216\) −2.90291 24.9143i −0.197518 1.69521i
\(217\) −18.3780 3.61617i −1.24758 0.245481i
\(218\) 19.1049 11.0302i 1.29395 0.747062i
\(219\) 0.262021 + 6.77346i 0.0177058 + 0.457708i
\(220\) 17.4198i 1.17444i
\(221\) 14.0204i 0.943117i
\(222\) −18.5537 + 11.6908i −1.24524 + 0.784634i
\(223\) −2.92075 + 1.68630i −0.195588 + 0.112923i −0.594596 0.804025i \(-0.702688\pi\)
0.399008 + 0.916947i \(0.369355\pi\)
\(224\) 0.634534 + 0.124855i 0.0423966 + 0.00834223i
\(225\) 2.99103 0.231754i 0.199402 0.0154503i
\(226\) 16.0929 27.8737i 1.07048 1.85413i
\(227\) 9.68429 16.7737i 0.642769 1.11331i −0.342043 0.939684i \(-0.611119\pi\)
0.984812 0.173624i \(-0.0555478\pi\)
\(228\) 22.4613 14.1530i 1.48754 0.937306i
\(229\) 9.06892 5.23594i 0.599291 0.346001i −0.169472 0.985535i \(-0.554206\pi\)
0.768763 + 0.639534i \(0.220873\pi\)
\(230\) 2.77269 4.80244i 0.182826 0.316663i
\(231\) −7.22454 18.7388i −0.475340 1.23292i
\(232\) 2.15076 + 3.72523i 0.141204 + 0.244573i
\(233\) 10.9648 + 6.33051i 0.718326 + 0.414726i 0.814136 0.580674i \(-0.197211\pi\)
−0.0958104 + 0.995400i \(0.530544\pi\)
\(234\) −13.0429 + 1.01060i −0.852639 + 0.0660650i
\(235\) −0.299936 0.519504i −0.0195656 0.0338887i
\(236\) 35.4895 2.31017
\(237\) 5.55070 10.5347i 0.360557 0.684299i
\(238\) −16.4368 48.0948i −1.06544 3.11752i
\(239\) 16.9811 + 9.80401i 1.09841 + 0.634169i 0.935804 0.352522i \(-0.114676\pi\)
0.162609 + 0.986691i \(0.448009\pi\)
\(240\) −6.66287 + 0.257743i −0.430086 + 0.0166373i
\(241\) −1.52294 0.879268i −0.0981009 0.0566386i 0.450147 0.892955i \(-0.351372\pi\)
−0.548248 + 0.836316i \(0.684705\pi\)
\(242\) 17.3720 10.0297i 1.11671 0.644735i
\(243\) 10.2426 + 11.7511i 0.657066 + 0.753833i
\(244\) 17.2676i 1.10544i
\(245\) 0.942339 + 6.93628i 0.0602038 + 0.443143i
\(246\) −12.8023 + 8.06682i −0.816246 + 0.514322i
\(247\) −3.43966 5.95767i −0.218861 0.379078i
\(248\) 34.1737 2.17004
\(249\) −10.7123 + 0.414388i −0.678862 + 0.0262608i
\(250\) 2.44435i 0.154594i
\(251\) −7.21616 −0.455480 −0.227740 0.973722i \(-0.573134\pi\)
−0.227740 + 0.973722i \(0.573134\pi\)
\(252\) 28.9766 12.4786i 1.82535 0.786081i
\(253\) −9.94241 −0.625074
\(254\) 7.73598i 0.485399i
\(255\) −7.25679 11.5168i −0.454438 0.721208i
\(256\) −31.7837 −1.98648
\(257\) −6.76721 11.7212i −0.422127 0.731146i 0.574020 0.818841i \(-0.305383\pi\)
−0.996147 + 0.0876955i \(0.972050\pi\)
\(258\) −0.879654 22.7398i −0.0547649 1.41572i
\(259\) −10.3221 9.01461i −0.641385 0.560141i
\(260\) 7.09101i 0.439766i
\(261\) −2.41149 1.15381i −0.149267 0.0714189i
\(262\) −12.4527 + 7.18960i −0.769333 + 0.444175i
\(263\) −3.78633 2.18604i −0.233475 0.134797i 0.378699 0.925520i \(-0.376372\pi\)
−0.612174 + 0.790723i \(0.709705\pi\)
\(264\) 19.5340 + 31.0011i 1.20223 + 1.90798i
\(265\) −11.9100 6.87623i −0.731624 0.422404i
\(266\) 18.7837 + 16.4043i 1.15170 + 1.00581i
\(267\) 3.12130 + 4.95361i 0.191021 + 0.303156i
\(268\) 25.7855 1.57510
\(269\) −10.5229 18.2262i −0.641592 1.11127i −0.985077 0.172112i \(-0.944941\pi\)
0.343486 0.939158i \(-0.388392\pi\)
\(270\) 10.1907 7.58094i 0.620185 0.461361i
\(271\) 2.86462 + 1.65389i 0.174013 + 0.100467i 0.584477 0.811410i \(-0.301300\pi\)
−0.410464 + 0.911877i \(0.634633\pi\)
\(272\) 15.1276 + 26.2017i 0.917243 + 1.58871i
\(273\) −2.94086 7.62791i −0.177989 0.461662i
\(274\) 0.608433 1.05384i 0.0367568 0.0636646i
\(275\) −3.79537 + 2.19126i −0.228870 + 0.132138i
\(276\) −0.603740 15.6072i −0.0363409 0.939440i
\(277\) 12.7847 22.1438i 0.768159 1.33049i −0.170401 0.985375i \(-0.554506\pi\)
0.938560 0.345116i \(-0.112160\pi\)
\(278\) −13.7976 + 23.8982i −0.827525 + 1.43332i
\(279\) −17.5175 + 12.0083i −1.04875 + 0.718915i
\(280\) −4.13026 12.0853i −0.246830 0.722234i
\(281\) 5.65129 3.26278i 0.337128 0.194641i −0.321873 0.946783i \(-0.604313\pi\)
0.659001 + 0.752142i \(0.270979\pi\)
\(282\) −2.24688 1.18388i −0.133800 0.0704991i
\(283\) 4.69297i 0.278968i 0.990224 + 0.139484i \(0.0445444\pi\)
−0.990224 + 0.139484i \(0.955456\pi\)
\(284\) 1.36729i 0.0811340i
\(285\) 5.90904 + 3.11347i 0.350022 + 0.184426i
\(286\) 16.5503 9.55532i 0.978639 0.565018i
\(287\) −7.12242 6.22022i −0.420423 0.367168i
\(288\) 0.604826 0.414608i 0.0356397 0.0244310i
\(289\) −22.3828 + 38.7682i −1.31664 + 2.28048i
\(290\) −1.08908 + 1.88634i −0.0639530 + 0.110770i
\(291\) 0.797045 + 20.6043i 0.0467236 + 1.20784i
\(292\) 13.4718 7.77794i 0.788376 0.455169i
\(293\) −5.27136 + 9.13027i −0.307956 + 0.533396i −0.977915 0.209002i \(-0.932978\pi\)
0.669959 + 0.742398i \(0.266312\pi\)
\(294\) 19.0307 + 22.7186i 1.10989 + 1.32497i
\(295\) 4.46426 + 7.73233i 0.259919 + 0.450194i
\(296\) 21.6539 + 12.5019i 1.25861 + 0.726657i
\(297\) −20.9066 9.02720i −1.21312 0.523811i
\(298\) 13.7660 + 23.8433i 0.797441 + 1.38121i
\(299\) −4.04721 −0.234056
\(300\) −3.67021 5.82475i −0.211900 0.336292i
\(301\) 13.4570 4.59905i 0.775649 0.265085i
\(302\) −4.94134 2.85288i −0.284342 0.164165i
\(303\) 15.5629 + 24.6988i 0.894063 + 1.41891i
\(304\) −12.8562 7.42255i −0.737356 0.425712i
\(305\) 3.76221 2.17211i 0.215423 0.124375i
\(306\) −51.9870 24.8739i −2.97190 1.42195i
\(307\) 12.9619i 0.739776i −0.929076 0.369888i \(-0.879396\pi\)
0.929076 0.369888i \(-0.120604\pi\)
\(308\) −30.3166 + 34.7138i −1.72745 + 1.97801i
\(309\) −0.890496 23.0200i −0.0506585 1.30956i
\(310\) 8.65227 + 14.9862i 0.491416 + 0.851158i
\(311\) −11.3292 −0.642418 −0.321209 0.947008i \(-0.604089\pi\)
−0.321209 + 0.947008i \(0.604089\pi\)
\(312\) 7.95161 + 12.6195i 0.450171 + 0.714437i
\(313\) 5.07321i 0.286755i −0.989668 0.143377i \(-0.954204\pi\)
0.989668 0.143377i \(-0.0457963\pi\)
\(314\) 58.6906 3.31210
\(315\) 6.36381 + 4.74362i 0.358560 + 0.267273i
\(316\) −27.3263 −1.53722
\(317\) 9.97253i 0.560113i 0.959984 + 0.280056i \(0.0903532\pi\)
−0.959984 + 0.280056i \(0.909647\pi\)
\(318\) −58.1808 + 2.25064i −3.26262 + 0.126210i
\(319\) 3.90527 0.218653
\(320\) −4.14842 7.18528i −0.231904 0.401669i
\(321\) 28.4824 17.9469i 1.58973 1.00170i
\(322\) 13.8833 4.74474i 0.773686 0.264414i
\(323\) 30.3062i 1.68628i
\(324\) 12.9010 33.3664i 0.716721 1.85369i
\(325\) −1.54497 + 0.891986i −0.0856993 + 0.0494785i
\(326\) −25.8534 14.9264i −1.43189 0.826699i
\(327\) 15.6202 0.604246i 0.863801 0.0334149i
\(328\) 14.9415 + 8.62648i 0.825007 + 0.476318i
\(329\) 0.306415 1.55725i 0.0168932 0.0858540i
\(330\) −8.64915 + 16.4152i −0.476120 + 0.903627i
\(331\) −25.0196 −1.37520 −0.687600 0.726089i \(-0.741336\pi\)
−0.687600 + 0.726089i \(0.741336\pi\)
\(332\) 12.3008 + 21.3057i 0.675097 + 1.16930i
\(333\) −15.4928 + 1.20043i −0.849002 + 0.0657832i
\(334\) 34.5605 + 19.9535i 1.89107 + 1.09181i
\(335\) 3.24358 + 5.61805i 0.177216 + 0.306947i
\(336\) −13.7262 11.0821i −0.748825 0.604579i
\(337\) −8.94751 + 15.4975i −0.487402 + 0.844205i −0.999895 0.0144863i \(-0.995389\pi\)
0.512493 + 0.858691i \(0.328722\pi\)
\(338\) −20.7822 + 11.9986i −1.13040 + 0.652639i
\(339\) 19.2956 12.1583i 1.04799 0.660346i
\(340\) −15.6194 + 27.0535i −0.847079 + 1.46718i
\(341\) 15.5128 26.8690i 0.840066 1.45504i
\(342\) 28.1931 2.18448i 1.52451 0.118123i
\(343\) −10.1937 + 15.4625i −0.550409 + 0.834895i
\(344\) −22.4705 + 12.9734i −1.21153 + 0.699477i
\(345\) 3.32449 2.09478i 0.178984 0.112779i
\(346\) 10.9989i 0.591302i
\(347\) 26.5501i 1.42528i 0.701528 + 0.712642i \(0.252502\pi\)
−0.701528 + 0.712642i \(0.747498\pi\)
\(348\) 0.237142 + 6.13031i 0.0127122 + 0.328619i
\(349\) −9.98709 + 5.76605i −0.534597 + 0.308649i −0.742886 0.669418i \(-0.766544\pi\)
0.208290 + 0.978067i \(0.433210\pi\)
\(350\) 4.25403 4.87105i 0.227388 0.260368i
\(351\) −8.51034 3.67466i −0.454248 0.196139i
\(352\) −0.535609 + 0.927703i −0.0285481 + 0.0494467i
\(353\) −13.3299 + 23.0881i −0.709480 + 1.22886i 0.255570 + 0.966791i \(0.417737\pi\)
−0.965050 + 0.262065i \(0.915596\pi\)
\(354\) 33.4428 + 17.6210i 1.77746 + 0.936544i
\(355\) 0.297901 0.171993i 0.0158110 0.00912847i
\(356\) 6.71823 11.6363i 0.356065 0.616723i
\(357\) 5.58207 35.5798i 0.295434 1.88308i
\(358\) −10.4501 18.1001i −0.552306 0.956622i
\(359\) −17.8292 10.2937i −0.940992 0.543282i −0.0507207 0.998713i \(-0.516152\pi\)
−0.890271 + 0.455431i \(0.849485\pi\)
\(360\) −13.0633 6.25032i −0.688498 0.329421i
\(361\) −2.06492 3.57655i −0.108680 0.188239i
\(362\) 2.13362 0.112141
\(363\) 14.2034 0.549437i 0.745484 0.0288380i
\(364\) −12.3409 + 14.1308i −0.646837 + 0.740656i
\(365\) 3.38926 + 1.95679i 0.177402 + 0.102423i
\(366\) 8.57357 16.2718i 0.448148 0.850538i
\(367\) 15.6251 + 9.02113i 0.815621 + 0.470899i 0.848904 0.528547i \(-0.177263\pi\)
−0.0332829 + 0.999446i \(0.510596\pi\)
\(368\) −7.56352 + 4.36680i −0.394276 + 0.227635i
\(369\) −10.6903 + 0.828316i −0.556514 + 0.0431204i
\(370\) 12.6611i 0.658221i
\(371\) −11.7669 34.4304i −0.610907 1.78754i
\(372\) 43.1197 + 22.7198i 2.23565 + 1.17796i
\(373\) 4.77327 + 8.26755i 0.247151 + 0.428078i 0.962734 0.270450i \(-0.0871724\pi\)
−0.715583 + 0.698527i \(0.753839\pi\)
\(374\) 84.1900 4.35336
\(375\) 0.807396 1.53235i 0.0416938 0.0791305i
\(376\) 2.89570i 0.149334i
\(377\) 1.58970 0.0818737
\(378\) 33.5013 + 2.62825i 1.72312 + 0.135183i
\(379\) 0.905456 0.0465101 0.0232551 0.999730i \(-0.492597\pi\)
0.0232551 + 0.999730i \(0.492597\pi\)
\(380\) 15.3277i 0.786296i
\(381\) 2.55528 4.84966i 0.130911 0.248456i
\(382\) 37.9520 1.94179
\(383\) −3.06888 5.31546i −0.156812 0.271607i 0.776905 0.629618i \(-0.216788\pi\)
−0.933718 + 0.358011i \(0.883455\pi\)
\(384\) −30.3276 15.9796i −1.54765 0.815456i
\(385\) −11.3769 2.23859i −0.579821 0.114089i
\(386\) 25.6998i 1.30808i
\(387\) 6.95975 14.5460i 0.353784 0.739417i
\(388\) 40.9800 23.6598i 2.08044 1.20114i
\(389\) −7.24609 4.18353i −0.367391 0.212114i 0.304927 0.952376i \(-0.401368\pi\)
−0.672318 + 0.740262i \(0.734701\pi\)
\(390\) −3.52077 + 6.68207i −0.178281 + 0.338360i
\(391\) −15.4409 8.91480i −0.780879 0.450841i
\(392\) 12.8020 31.2714i 0.646598 1.57945i
\(393\) −10.1814 + 0.393852i −0.513583 + 0.0198672i
\(394\) 15.1140 0.761433
\(395\) −3.43741 5.95376i −0.172955 0.299566i
\(396\) 4.03712 + 52.1033i 0.202873 + 2.61829i
\(397\) −17.1060 9.87616i −0.858526 0.495670i 0.00499248 0.999988i \(-0.498411\pi\)
−0.863518 + 0.504317i \(0.831744\pi\)
\(398\) −16.2413 28.1307i −0.814101 1.41006i
\(399\) 6.35688 + 16.4883i 0.318242 + 0.825447i
\(400\) −1.92484 + 3.33393i −0.0962422 + 0.166696i
\(401\) −13.3743 + 7.72163i −0.667879 + 0.385600i −0.795272 0.606252i \(-0.792672\pi\)
0.127394 + 0.991852i \(0.459339\pi\)
\(402\) 24.2984 + 12.8028i 1.21189 + 0.638546i
\(403\) 6.31474 10.9374i 0.314559 0.544833i
\(404\) 33.4972 58.0188i 1.66655 2.88654i
\(405\) 8.89258 1.38637i 0.441876 0.0688893i
\(406\) −5.45320 + 1.86368i −0.270638 + 0.0924929i
\(407\) 19.6591 11.3502i 0.974466 0.562608i
\(408\) 2.53999 + 65.6606i 0.125748 + 3.25069i
\(409\) 4.73802i 0.234280i 0.993115 + 0.117140i \(0.0373726\pi\)
−0.993115 + 0.117140i \(0.962627\pi\)
\(410\) 8.73638i 0.431459i
\(411\) 0.729519 0.459675i 0.0359845 0.0226741i
\(412\) −45.7847 + 26.4338i −2.25565 + 1.30230i
\(413\) −4.56070 + 23.1782i −0.224417 + 1.14053i
\(414\) 7.18022 15.0068i 0.352889 0.737546i
\(415\) −3.09467 + 5.36013i −0.151912 + 0.263119i
\(416\) −0.218028 + 0.377636i −0.0106897 + 0.0185151i
\(417\) −16.5435 + 10.4242i −0.810139 + 0.510474i
\(418\) −35.7746 + 20.6545i −1.74980 + 1.01024i
\(419\) −0.120202 + 0.208195i −0.00587224 + 0.0101710i −0.868947 0.494906i \(-0.835203\pi\)
0.863074 + 0.505077i \(0.168536\pi\)
\(420\) 2.82320 17.9949i 0.137758 0.878061i
\(421\) 6.23154 + 10.7933i 0.303707 + 0.526035i 0.976973 0.213365i \(-0.0684424\pi\)
−0.673266 + 0.739400i \(0.735109\pi\)
\(422\) −33.0018 19.0536i −1.60650 0.927515i
\(423\) −1.01752 1.48434i −0.0494733 0.0721712i
\(424\) 33.1930 + 57.4919i 1.61199 + 2.79205i
\(425\) −7.85911 −0.381223
\(426\) 0.678878 1.28844i 0.0328918 0.0624252i
\(427\) 11.2775 + 2.21903i 0.545756 + 0.107386i
\(428\) −66.9067 38.6286i −3.23406 1.86719i
\(429\) 13.5316 0.523448i 0.653310 0.0252723i
\(430\) −11.3784 6.56931i −0.548715 0.316800i
\(431\) 1.71946 0.992731i 0.0828235 0.0478182i −0.458016 0.888944i \(-0.651440\pi\)
0.540840 + 0.841126i \(0.318107\pi\)
\(432\) −19.8691 + 2.31507i −0.955955 + 0.111384i
\(433\) 31.7870i 1.52758i 0.645463 + 0.763792i \(0.276665\pi\)
−0.645463 + 0.763792i \(0.723335\pi\)
\(434\) −8.83918 + 44.9222i −0.424294 + 2.15633i
\(435\) −1.30582 + 0.822807i −0.0626094 + 0.0394506i
\(436\) −17.9367 31.0672i −0.859010 1.48785i
\(437\) 8.74834 0.418490
\(438\) 16.5567 0.640471i 0.791110 0.0306029i
\(439\) 7.36913i 0.351709i 0.984416 + 0.175855i \(0.0562689\pi\)
−0.984416 + 0.175855i \(0.943731\pi\)
\(440\) 21.1553 1.00854
\(441\) 4.42608 + 20.5283i 0.210766 + 0.977537i
\(442\) 34.2709 1.63010
\(443\) 41.1425i 1.95474i −0.211537 0.977370i \(-0.567847\pi\)
0.211537 0.977370i \(-0.432153\pi\)
\(444\) 19.0108 + 30.1708i 0.902213 + 1.43184i
\(445\) 3.38038 0.160245
\(446\) 4.12190 + 7.13934i 0.195177 + 0.338057i
\(447\) 0.754111 + 19.4944i 0.0356682 + 0.922052i
\(448\) 4.23804 21.5384i 0.200228 1.01759i
\(449\) 26.0169i 1.22781i 0.789379 + 0.613906i \(0.210403\pi\)
−0.789379 + 0.613906i \(0.789597\pi\)
\(450\) −0.566489 7.31113i −0.0267045 0.344650i
\(451\) 13.5651 7.83180i 0.638755 0.368785i
\(452\) −45.3264 26.1692i −2.13197 1.23090i
\(453\) −2.15537 3.42064i −0.101268 0.160716i
\(454\) −41.0007 23.6718i −1.92426 1.11097i
\(455\) −4.63115 0.911255i −0.217112 0.0427203i
\(456\) −17.1880 27.2779i −0.804900 1.27740i
\(457\) −30.7128 −1.43668 −0.718342 0.695690i \(-0.755099\pi\)
−0.718342 + 0.695690i \(0.755099\pi\)
\(458\) −12.7985 22.1676i −0.598033 1.03582i
\(459\) −24.3744 32.7653i −1.13770 1.52935i
\(460\) −7.80941 4.50877i −0.364116 0.210222i
\(461\) −15.7774 27.3273i −0.734828 1.27276i −0.954799 0.297253i \(-0.903930\pi\)
0.219971 0.975506i \(-0.429404\pi\)
\(462\) −45.8041 + 17.6593i −2.13100 + 0.821584i
\(463\) −12.2485 + 21.2150i −0.569234 + 0.985943i 0.427408 + 0.904059i \(0.359427\pi\)
−0.996642 + 0.0818837i \(0.973906\pi\)
\(464\) 2.97086 1.71523i 0.137919 0.0796275i
\(465\) 0.473979 + 12.2527i 0.0219802 + 0.568207i
\(466\) 15.4740 26.8017i 0.716818 1.24157i
\(467\) 1.33602 2.31405i 0.0618236 0.107082i −0.833457 0.552584i \(-0.813642\pi\)
0.895281 + 0.445503i \(0.146975\pi\)
\(468\) 1.64337 + 21.2095i 0.0759649 + 0.980408i
\(469\) −3.31365 + 16.8405i −0.153010 + 0.777623i
\(470\) −1.26985 + 0.733147i −0.0585737 + 0.0338176i
\(471\) 36.7929 + 19.3862i 1.69533 + 0.893267i
\(472\) 43.0998i 1.98383i
\(473\) 23.5565i 1.08313i
\(474\) −25.7504 13.5678i −1.18275 0.623192i
\(475\) 3.33955 1.92809i 0.153229 0.0884669i
\(476\) −78.2087 + 26.7285i −3.58469 + 1.22510i
\(477\) −37.2168 17.8069i −1.70404 0.815320i
\(478\) 23.9644 41.5076i 1.09611 1.89851i
\(479\) −1.78583 + 3.09315i −0.0815968 + 0.141330i −0.903936 0.427668i \(-0.859335\pi\)
0.822339 + 0.568998i \(0.192669\pi\)
\(480\) −0.0163650 0.423049i −0.000746957 0.0193094i
\(481\) 8.00255 4.62027i 0.364885 0.210666i
\(482\) −2.14924 + 3.72259i −0.0978951 + 0.169559i
\(483\) 10.2706 + 1.61135i 0.467330 + 0.0733189i
\(484\) −16.3097 28.2492i −0.741350 1.28406i
\(485\) 10.3098 + 5.95238i 0.468145 + 0.270284i
\(486\) 28.7238 25.0366i 1.30294 1.13568i
\(487\) −8.17684 14.1627i −0.370528 0.641773i 0.619119 0.785297i \(-0.287490\pi\)
−0.989647 + 0.143524i \(0.954157\pi\)
\(488\) −20.9704 −0.949287
\(489\) −11.2770 17.8970i −0.509964 0.809330i
\(490\) 16.9547 2.30340i 0.765935 0.104057i
\(491\) −36.3236 20.9714i −1.63926 0.946427i −0.981089 0.193559i \(-0.937997\pi\)
−0.658172 0.752868i \(-0.728670\pi\)
\(492\) 13.1177 + 20.8183i 0.591394 + 0.938561i
\(493\) 6.06500 + 3.50163i 0.273154 + 0.157706i
\(494\) −14.5626 + 8.40774i −0.655204 + 0.378282i
\(495\) −10.8443 + 7.43373i −0.487413 + 0.334121i
\(496\) 27.2535i 1.22372i
\(497\) 0.892981 + 0.175709i 0.0400557 + 0.00788162i
\(498\) 1.01291 + 26.1845i 0.0453895 + 1.17336i
\(499\) 15.5412 + 26.9181i 0.695718 + 1.20502i 0.969938 + 0.243352i \(0.0782470\pi\)
−0.274220 + 0.961667i \(0.588420\pi\)
\(500\) −3.97484 −0.177760
\(501\) 15.0750 + 23.9245i 0.673501 + 1.06887i
\(502\) 17.6388i 0.787259i
\(503\) −16.2335 −0.723815 −0.361908 0.932214i \(-0.617874\pi\)
−0.361908 + 0.932214i \(0.617874\pi\)
\(504\) −15.1546 35.1903i −0.675038 1.56750i
\(505\) 16.8546 0.750020
\(506\) 24.3027i 1.08039i
\(507\) −16.9916 + 0.657295i −0.754623 + 0.0291915i
\(508\) −12.5798 −0.558136
\(509\) −6.36136 11.0182i −0.281962 0.488373i 0.689906 0.723899i \(-0.257652\pi\)
−0.971868 + 0.235526i \(0.924319\pi\)
\(510\) −28.1510 + 17.7381i −1.24655 + 0.785458i
\(511\) 3.34854 + 9.79797i 0.148131 + 0.433437i
\(512\) 38.1074i 1.68413i
\(513\) 18.3957 + 7.94305i 0.812191 + 0.350694i
\(514\) −28.6506 + 16.5414i −1.26372 + 0.729611i
\(515\) −11.5186 6.65028i −0.507571 0.293046i
\(516\) −36.9779 + 1.43044i −1.62786 + 0.0629715i
\(517\) 2.27673 + 1.31447i 0.100131 + 0.0578105i
\(518\) −22.0349 + 25.2309i −0.968156 + 1.10858i
\(519\) 3.63305 6.89515i 0.159473 0.302663i
\(520\) 8.61160 0.377644
\(521\) 3.53054 + 6.11507i 0.154676 + 0.267906i 0.932941 0.360030i \(-0.117233\pi\)
−0.778265 + 0.627936i \(0.783900\pi\)
\(522\) −2.82031 + 5.89452i −0.123442 + 0.257996i
\(523\) 22.9186 + 13.2321i 1.00216 + 0.578598i 0.908887 0.417043i \(-0.136934\pi\)
0.0932737 + 0.995641i \(0.470267\pi\)
\(524\) 11.6913 + 20.2498i 0.510735 + 0.884619i
\(525\) 4.27580 1.64849i 0.186611 0.0719460i
\(526\) −5.34345 + 9.25512i −0.232985 + 0.403542i
\(527\) 48.1838 27.8189i 2.09892 1.21181i
\(528\) 24.7233 15.5783i 1.07594 0.677959i
\(529\) −8.92661 + 15.4613i −0.388113 + 0.672232i
\(530\) −16.8079 + 29.1122i −0.730089 + 1.26455i
\(531\) 15.1448 + 22.0931i 0.657227 + 0.958757i
\(532\) 26.6757 30.5448i 1.15654 1.32428i
\(533\) 5.52188 3.18806i 0.239179 0.138090i
\(534\) 12.1084 7.62956i 0.523980 0.330163i
\(535\) 19.4366i 0.840316i
\(536\) 31.3149i 1.35260i
\(537\) −0.572466 14.7987i −0.0247037 0.638611i
\(538\) −44.5511 + 25.7216i −1.92074 + 1.10894i
\(539\) −18.7757 24.2609i −0.808727 1.04499i
\(540\) −12.3276 16.5714i −0.530497 0.713121i
\(541\) 16.1875 28.0376i 0.695955 1.20543i −0.273903 0.961757i \(-0.588315\pi\)
0.969858 0.243672i \(-0.0783520\pi\)
\(542\) 4.04269 7.00214i 0.173648 0.300768i
\(543\) 1.33756 + 0.704759i 0.0574002 + 0.0302441i
\(544\) −1.66364 + 0.960501i −0.0713279 + 0.0411812i
\(545\) 4.51255 7.81596i 0.193296 0.334799i
\(546\) −18.6453 + 7.18849i −0.797944 + 0.307639i
\(547\) −2.71649 4.70510i −0.116149 0.201176i 0.802090 0.597204i \(-0.203722\pi\)
−0.918238 + 0.396028i \(0.870388\pi\)
\(548\) −1.71368 0.989394i −0.0732048 0.0422648i
\(549\) 10.7495 7.36877i 0.458777 0.314491i
\(550\) 5.35620 + 9.27721i 0.228389 + 0.395582i
\(551\) −3.43625 −0.146389
\(552\) −18.9539 + 0.733205i −0.806733 + 0.0312073i
\(553\) 3.51166 17.8468i 0.149331 0.758925i
\(554\) −54.1271 31.2503i −2.29964 1.32770i
\(555\) −4.18212 + 7.93723i −0.177521 + 0.336917i
\(556\) 38.8616 + 22.4368i 1.64810 + 0.951531i
\(557\) 22.1583 12.7931i 0.938878 0.542061i 0.0492696 0.998786i \(-0.484311\pi\)
0.889608 + 0.456724i \(0.150977\pi\)
\(558\) 29.3524 + 42.8190i 1.24258 + 1.81267i
\(559\) 9.58904i 0.405573i
\(560\) −9.63800 + 3.29387i −0.407280 + 0.139191i
\(561\) 52.7784 + 27.8089i 2.22831 + 1.17409i
\(562\) −7.97537 13.8137i −0.336420 0.582697i
\(563\) −14.7083 −0.619880 −0.309940 0.950756i \(-0.600309\pi\)
−0.309940 + 0.950756i \(0.600309\pi\)
\(564\) −1.92515 + 3.65374i −0.0810635 + 0.153850i
\(565\) 13.1674i 0.553957i
\(566\) 11.4713 0.482173
\(567\) 20.1337 + 12.7135i 0.845537 + 0.533917i
\(568\) −1.66050 −0.0696728
\(569\) 0.139959i 0.00586740i −0.999996 0.00293370i \(-0.999066\pi\)
0.999996 0.00293370i \(-0.000933826\pi\)
\(570\) 7.61040 14.4438i 0.318765 0.604983i
\(571\) 33.1340 1.38661 0.693307 0.720642i \(-0.256153\pi\)
0.693307 + 0.720642i \(0.256153\pi\)
\(572\) −15.5382 26.9130i −0.649686 1.12529i
\(573\) 23.7920 + 12.5360i 0.993924 + 0.523697i
\(574\) −15.2044 + 17.4097i −0.634619 + 0.726666i
\(575\) 2.26865i 0.0946093i
\(576\) −14.0733 20.5300i −0.586387 0.855417i
\(577\) 26.9549 15.5624i 1.12215 0.647871i 0.180198 0.983630i \(-0.442326\pi\)
0.941948 + 0.335759i \(0.108993\pi\)
\(578\) 94.7630 + 54.7115i 3.94162 + 2.27570i
\(579\) −8.48893 + 16.1111i −0.352788 + 0.669555i
\(580\) 3.06745 + 1.77099i 0.127369 + 0.0735365i
\(581\) −15.4955 + 5.29574i −0.642863 + 0.219704i
\(582\) 50.3640 1.94826i 2.08765 0.0807578i
\(583\) 60.2704 2.49615
\(584\) −9.44583 16.3607i −0.390871 0.677009i
\(585\) −4.41432 + 3.02601i −0.182510 + 0.125110i
\(586\) 22.3176 + 12.8851i 0.921930 + 0.532277i
\(587\) 9.74979 + 16.8871i 0.402417 + 0.697007i 0.994017 0.109225i \(-0.0348369\pi\)
−0.591600 + 0.806232i \(0.701504\pi\)
\(588\) 36.9435 30.9465i 1.52352 1.27621i
\(589\) −13.6498 + 23.6421i −0.562428 + 0.974154i
\(590\) 18.9005 10.9122i 0.778122 0.449249i
\(591\) 9.47493 + 4.99233i 0.389747 + 0.205357i
\(592\) 9.97022 17.2689i 0.409774 0.709749i
\(593\) −16.3836 + 28.3772i −0.672794 + 1.16531i 0.304314 + 0.952572i \(0.401573\pi\)
−0.977108 + 0.212742i \(0.931761\pi\)
\(594\) −22.0656 + 51.1029i −0.905364 + 2.09678i
\(595\) −15.6615 13.6776i −0.642058 0.560728i
\(596\) 38.7725 22.3853i 1.58818 0.916938i
\(597\) −0.889710 22.9997i −0.0364134 0.941316i
\(598\) 9.89280i 0.404547i
\(599\) 1.28048i 0.0523189i −0.999658 0.0261594i \(-0.991672\pi\)
0.999658 0.0261594i \(-0.00832776\pi\)
\(600\) −7.07380 + 4.45725i −0.288787 + 0.181966i
\(601\) −16.8456 + 9.72583i −0.687148 + 0.396725i −0.802543 0.596595i \(-0.796520\pi\)
0.115395 + 0.993320i \(0.463187\pi\)
\(602\) −11.2417 32.8936i −0.458177 1.34064i
\(603\) 11.0037 + 16.0521i 0.448105 + 0.653691i
\(604\) −4.63917 + 8.03529i −0.188765 + 0.326951i
\(605\) 4.10323 7.10700i 0.166820 0.288941i
\(606\) 60.3724 38.0411i 2.45246 1.54531i
\(607\) 19.6796 11.3620i 0.798772 0.461171i −0.0442698 0.999020i \(-0.514096\pi\)
0.843041 + 0.537849i \(0.180763\pi\)
\(608\) 0.471284 0.816287i 0.0191131 0.0331048i
\(609\) −4.03419 0.632919i −0.163474 0.0256472i
\(610\) −5.30940 9.19614i −0.214971 0.372341i
\(611\) 0.926781 + 0.535077i 0.0374935 + 0.0216469i
\(612\) −40.4483 + 84.5379i −1.63503 + 3.41724i
\(613\) −22.1377 38.3437i −0.894134 1.54869i −0.834873 0.550443i \(-0.814459\pi\)
−0.0592614 0.998242i \(-0.518875\pi\)
\(614\) −31.6835 −1.27864
\(615\) −2.88572 + 5.47681i −0.116364 + 0.220846i
\(616\) 42.1579 + 36.8177i 1.69859 + 1.48343i
\(617\) −5.53420 3.19517i −0.222798 0.128633i 0.384447 0.923147i \(-0.374392\pi\)
−0.607245 + 0.794514i \(0.707726\pi\)
\(618\) −56.2690 + 2.17668i −2.26347 + 0.0875590i
\(619\) 14.5285 + 8.38801i 0.583948 + 0.337143i 0.762701 0.646751i \(-0.223873\pi\)
−0.178753 + 0.983894i \(0.557206\pi\)
\(620\) 24.3695 14.0698i 0.978705 0.565055i
\(621\) 9.45819 7.03603i 0.379544 0.282346i
\(622\) 27.6924i 1.11036i
\(623\) 6.73634 + 5.88305i 0.269886 + 0.235699i
\(624\) 10.0640 6.34139i 0.402882 0.253859i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −12.4007 −0.495632
\(627\) −29.2494 + 1.13147i −1.16811 + 0.0451866i
\(628\) 95.4388i 3.80842i
\(629\) 40.7083 1.62315
\(630\) 11.5951 15.5554i 0.461959 0.619741i
\(631\) −12.0000 −0.477713 −0.238857 0.971055i \(-0.576773\pi\)
−0.238857 + 0.971055i \(0.576773\pi\)
\(632\) 33.1861i 1.32007i
\(633\) −14.3951 22.8455i −0.572154 0.908028i
\(634\) 24.3763 0.968108
\(635\) −1.58242 2.74083i −0.0627965 0.108767i
\(636\) 3.65984 + 94.6098i 0.145122 + 3.75152i
\(637\) −7.64295 9.87576i −0.302825 0.391292i
\(638\) 9.54583i 0.377923i
\(639\) 0.851173 0.583478i 0.0336719 0.0230821i
\(640\) −17.1400 + 9.89576i −0.677517 + 0.391164i
\(641\) 1.66913 + 0.963673i 0.0659267 + 0.0380628i 0.532601 0.846366i \(-0.321215\pi\)
−0.466674 + 0.884429i \(0.654548\pi\)
\(642\) −43.8686 69.6209i −1.73136 2.74772i
\(643\) 0.105313 + 0.0608025i 0.00415314 + 0.00239782i 0.502075 0.864824i \(-0.332570\pi\)
−0.497922 + 0.867222i \(0.665903\pi\)
\(644\) −7.71559 22.5761i −0.304037 0.889624i
\(645\) −4.96316 7.87669i −0.195424 0.310145i
\(646\) −74.0789 −2.91460
\(647\) 18.1842 + 31.4959i 0.714894 + 1.23823i 0.963000 + 0.269500i \(0.0868583\pi\)
−0.248107 + 0.968733i \(0.579808\pi\)
\(648\) −40.5214 15.6675i −1.59183 0.615476i
\(649\) −33.8871 19.5647i −1.33018 0.767982i
\(650\) 2.18033 + 3.77644i 0.0855194 + 0.148124i
\(651\) −20.3795 + 25.2419i −0.798738 + 0.989307i
\(652\) −24.2724 + 42.0411i −0.950581 + 1.64645i
\(653\) 32.1477 18.5605i 1.25804 0.726328i 0.285345 0.958425i \(-0.407892\pi\)
0.972693 + 0.232097i \(0.0745586\pi\)
\(654\) −1.47699 38.1813i −0.0577548 1.49301i
\(655\) −2.94131 + 5.09450i −0.114927 + 0.199059i
\(656\) 6.87960 11.9158i 0.268603 0.465235i
\(657\) 10.5909 + 5.06736i 0.413190 + 0.197696i
\(658\) −3.80646 0.748985i −0.148391 0.0291985i
\(659\) −34.3197 + 19.8145i −1.33691 + 0.771863i −0.986347 0.164677i \(-0.947342\pi\)
−0.350559 + 0.936541i \(0.614008\pi\)
\(660\) 26.6933 + 14.0647i 1.03904 + 0.547467i
\(661\) 18.6155i 0.724061i 0.932166 + 0.362030i \(0.117916\pi\)
−0.932166 + 0.362030i \(0.882084\pi\)
\(662\) 61.1566i 2.37692i
\(663\) 21.4843 + 11.3201i 0.834381 + 0.439635i
\(664\) 25.8745 14.9386i 1.00412 0.579731i
\(665\) 10.0106 + 1.96974i 0.388193 + 0.0763833i
\(666\) 2.93427 + 37.8699i 0.113701 + 1.46743i
\(667\) −1.01080 + 1.75075i −0.0391383 + 0.0677895i
\(668\) 32.4471 56.2001i 1.25542 2.17445i
\(669\) 0.225801 + 5.83714i 0.00872997 + 0.225677i
\(670\) 13.7325 7.92845i 0.530532 0.306303i
\(671\) −9.51931 + 16.4879i −0.367489 + 0.636510i
\(672\) 0.703642 0.871524i 0.0271436 0.0336198i
\(673\) 17.5049 + 30.3194i 0.674765 + 1.16873i 0.976538 + 0.215347i \(0.0690883\pi\)
−0.301773 + 0.953380i \(0.597578\pi\)
\(674\) 37.8814 + 21.8708i 1.45914 + 0.842433i
\(675\) 2.05982 4.77044i 0.0792825 0.183614i
\(676\) 19.5114 + 33.7947i 0.750438 + 1.29980i
\(677\) 42.2000 1.62188 0.810940 0.585130i \(-0.198956\pi\)
0.810940 + 0.585130i \(0.198956\pi\)
\(678\) −29.7190 47.1651i −1.14135 1.81136i
\(679\) 10.1860 + 29.8045i 0.390901 + 1.14379i
\(680\) 32.8549 + 18.9688i 1.25993 + 0.727419i
\(681\) −17.8842 28.3828i −0.685323 1.08763i
\(682\) −65.6772 37.9187i −2.51491 1.45198i
\(683\) −7.07680 + 4.08579i −0.270786 + 0.156339i −0.629245 0.777207i \(-0.716636\pi\)
0.358459 + 0.933546i \(0.383302\pi\)
\(684\) −3.55227 45.8458i −0.135824 1.75296i
\(685\) 0.497828i 0.0190210i
\(686\) 37.7957 + 24.9170i 1.44305 + 0.951335i
\(687\) −0.701111 18.1243i −0.0267491 0.691484i
\(688\) 10.3462 + 17.9202i 0.394446 + 0.683201i
\(689\) 24.5340 0.934672
\(690\) −5.12038 8.12621i −0.194929 0.309360i
\(691\) 37.7671i 1.43673i −0.695668 0.718364i \(-0.744891\pi\)
0.695668 0.718364i \(-0.255109\pi\)
\(692\) −17.8856 −0.679910
\(693\) −34.5475 4.05906i −1.31235 0.154191i
\(694\) 64.8977 2.46348
\(695\) 11.2894i 0.428231i
\(696\) 7.44489 0.287995i 0.282198 0.0109164i
\(697\) 28.0894 1.06396
\(698\) 14.0942 + 24.4119i 0.533475 + 0.924005i
\(699\) 18.5535 11.6907i 0.701758 0.442182i
\(700\) −7.92098 6.91763i −0.299385 0.261462i
\(701\) 35.4760i 1.33991i 0.742402 + 0.669954i \(0.233686\pi\)
−0.742402 + 0.669954i \(0.766314\pi\)
\(702\) −8.98216 + 20.8022i −0.339010 + 0.785130i
\(703\) −17.2981 + 9.98705i −0.652410 + 0.376669i
\(704\) 31.4896 + 18.1805i 1.18681 + 0.685205i
\(705\) −1.03823 + 0.0401624i −0.0391020 + 0.00151260i
\(706\) 56.4354 + 32.5830i 2.12397 + 1.22628i
\(707\) 33.5875 + 29.3330i 1.26319 + 1.10318i
\(708\) 28.6541 54.3825i 1.07689 2.04382i
\(709\) 0.383803 0.0144140 0.00720701 0.999974i \(-0.497706\pi\)
0.00720701 + 0.999974i \(0.497706\pi\)
\(710\) −0.420412 0.728175i −0.0157778 0.0273279i
\(711\) −11.6612 17.0113i −0.437330 0.637973i
\(712\) −14.1316 8.15888i −0.529604 0.305767i
\(713\) 8.03036 + 13.9090i 0.300739 + 0.520896i
\(714\) −86.9694 13.6445i −3.25475 0.510633i
\(715\) 3.90915 6.77084i 0.146194 0.253215i
\(716\) −29.4333 + 16.9933i −1.09997 + 0.635070i
\(717\) 28.7337 18.1053i 1.07308 0.676154i
\(718\) −25.1614 + 43.5809i −0.939017 + 1.62642i
\(719\) −20.4550 + 35.4291i −0.762842 + 1.32128i 0.178537 + 0.983933i \(0.442863\pi\)
−0.941380 + 0.337349i \(0.890470\pi\)
\(720\) −4.98462 + 10.4180i −0.185766 + 0.388255i
\(721\) −11.3802 33.2990i −0.423822 1.24012i
\(722\) −8.74233 + 5.04739i −0.325356 + 0.187844i
\(723\) −2.57696 + 1.62376i −0.0958383 + 0.0603883i
\(724\) 3.46956i 0.128945i
\(725\) 0.891101i 0.0330947i
\(726\) −1.34302 34.7180i −0.0498440 1.28851i
\(727\) 0.765637 0.442041i 0.0283959 0.0163944i −0.485735 0.874106i \(-0.661448\pi\)
0.514131 + 0.857712i \(0.328115\pi\)
\(728\) 17.1610 + 14.9872i 0.636030 + 0.555464i
\(729\) 26.2767 6.20758i 0.973212 0.229910i
\(730\) 4.78308 8.28454i 0.177030 0.306625i
\(731\) −21.1218 + 36.5840i −0.781217 + 1.35311i
\(732\) −26.4601 13.9418i −0.977993 0.515303i
\(733\) 35.9939 20.7811i 1.32946 0.767566i 0.344247 0.938879i \(-0.388134\pi\)
0.985217 + 0.171313i \(0.0548009\pi\)
\(734\) 22.0508 38.1931i 0.813909 1.40973i
\(735\) 11.3897 + 4.15633i 0.420115 + 0.153309i
\(736\) −0.277263 0.480234i −0.0102201 0.0177017i
\(737\) −24.6212 14.2151i −0.906934 0.523619i
\(738\) 2.02469 + 26.1308i 0.0745300 + 0.961888i
\(739\) −7.43979 12.8861i −0.273677 0.474023i 0.696123 0.717922i \(-0.254907\pi\)
−0.969800 + 0.243900i \(0.921573\pi\)
\(740\) 20.5887 0.756857
\(741\) −11.9064 + 0.460583i −0.437394 + 0.0169199i
\(742\) −84.1599 + 28.7624i −3.08961 + 1.05590i
\(743\) 2.00964 + 1.16027i 0.0737265 + 0.0425660i 0.536410 0.843957i \(-0.319780\pi\)
−0.462684 + 0.886523i \(0.653113\pi\)
\(744\) 27.5918 52.3663i 1.01156 1.91984i
\(745\) 9.75448 + 5.63175i 0.357376 + 0.206331i
\(746\) 20.2088 11.6675i 0.739896 0.427179i
\(747\) −8.01405 + 16.7496i −0.293219 + 0.612834i
\(748\) 136.904i 5.00572i
\(749\) 33.8265 38.7328i 1.23599 1.41526i
\(750\) −3.74561 1.97356i −0.136770 0.0720642i
\(751\) −16.4458 28.4850i −0.600116 1.03943i −0.992803 0.119760i \(-0.961788\pi\)
0.392686 0.919672i \(-0.371546\pi\)
\(752\) 2.30932 0.0842121
\(753\) −5.82630 + 11.0577i −0.212322 + 0.402966i
\(754\) 3.88578i 0.141512i
\(755\) −2.33427 −0.0849527
\(756\) 4.27389 54.4777i 0.155440 1.98133i
\(757\) −18.8340 −0.684535 −0.342268 0.939603i \(-0.611195\pi\)
−0.342268 + 0.939603i \(0.611195\pi\)
\(758\) 2.21325i 0.0803889i
\(759\) −8.02746 + 15.2353i −0.291378 + 0.553006i
\(760\) −18.6146 −0.675222
\(761\) −4.75297 8.23238i −0.172295 0.298423i 0.766927 0.641734i \(-0.221785\pi\)
−0.939222 + 0.343311i \(0.888452\pi\)
\(762\) −11.8543 6.24600i −0.429435 0.226269i
\(763\) 22.5950 7.72206i 0.817995 0.279557i
\(764\) 61.7150i 2.23277i
\(765\) −23.5069 + 1.82138i −0.849893 + 0.0658523i
\(766\) −12.9928 + 7.50142i −0.469450 + 0.271037i
\(767\) −13.7943 7.96412i −0.498082 0.287568i
\(768\) −25.6620 + 48.7039i −0.925999 + 1.75745i
\(769\) 14.2817 + 8.24557i 0.515013 + 0.297343i 0.734892 0.678184i \(-0.237233\pi\)
−0.219879 + 0.975527i \(0.570566\pi\)
\(770\) −5.47190 + 27.8091i −0.197194 + 1.00217i
\(771\) −23.4248 + 0.906154i −0.843623 + 0.0326343i
\(772\) 41.7913 1.50410
\(773\) −19.5007 33.7762i −0.701392 1.21485i −0.967978 0.251036i \(-0.919229\pi\)
0.266585 0.963811i \(-0.414105\pi\)
\(774\) −35.5556 17.0121i −1.27802 0.611486i
\(775\) 6.13095 + 3.53970i 0.220230 + 0.127150i
\(776\) −28.7334 49.7677i −1.03147 1.78655i
\(777\) −22.1476 + 8.53878i −0.794542 + 0.306327i
\(778\) −10.2260 + 17.7120i −0.366620 + 0.635005i
\(779\) −11.9359 + 6.89122i −0.427649 + 0.246903i
\(780\) 10.8659 + 5.72526i 0.389063 + 0.204997i
\(781\) −0.753764 + 1.30556i −0.0269718 + 0.0467166i
\(782\) −21.7909 + 37.7429i −0.779240 + 1.34968i
\(783\) −3.71507 + 2.76367i −0.132766 + 0.0987657i
\(784\) −24.9389 10.2096i −0.890675 0.364627i
\(785\) 20.7939 12.0054i 0.742166 0.428490i
\(786\) 0.962712 + 24.8869i 0.0343388 + 0.887685i
\(787\) 37.9768i 1.35373i −0.736108 0.676864i \(-0.763338\pi\)
0.736108 0.676864i \(-0.236662\pi\)
\(788\) 24.5774i 0.875535i
\(789\) −6.40686 + 4.03700i −0.228090 + 0.143721i
\(790\) −14.5531 + 8.40222i −0.517775 + 0.298938i
\(791\) 22.9160 26.2397i 0.814798 0.932978i
\(792\) 63.2763 4.90283i 2.24842 0.174215i
\(793\) −3.87499 + 6.71167i −0.137605 + 0.238338i
\(794\) −24.1408 + 41.8131i −0.856724 + 1.48389i
\(795\) −20.1529 + 12.6985i −0.714750 + 0.450369i
\(796\) −45.7443 + 26.4105i −1.62136 + 0.936095i
\(797\) 18.9269 32.7823i 0.670425 1.16121i −0.307359 0.951594i \(-0.599445\pi\)
0.977784 0.209616i \(-0.0672215\pi\)
\(798\) 40.3031 15.5384i 1.42671 0.550055i
\(799\) 2.35723 + 4.08284i 0.0833927 + 0.144440i
\(800\) −0.211683 0.122215i −0.00748411 0.00432095i
\(801\) 10.1108 0.783417i 0.357248 0.0276807i
\(802\) 18.8744 + 32.6914i 0.666477 + 1.15437i
\(803\) −17.1513 −0.605258
\(804\) 20.8191 39.5125i 0.734233 1.39350i
\(805\) 3.94826 4.52092i 0.139158 0.159342i
\(806\) −26.7349 15.4354i −0.941698 0.543689i
\(807\) −36.4251 + 1.40905i −1.28222 + 0.0496010i
\(808\) −70.4603 40.6803i −2.47879 1.43113i
\(809\) −45.8364 + 26.4637i −1.61152 + 0.930413i −0.622506 + 0.782615i \(0.713885\pi\)
−0.989018 + 0.147798i \(0.952781\pi\)
\(810\) −3.38877 21.7366i −0.119069 0.763745i
\(811\) 16.7360i 0.587682i −0.955854 0.293841i \(-0.905066\pi\)
0.955854 0.293841i \(-0.0949335\pi\)
\(812\) 3.03060 + 8.86764i 0.106353 + 0.311193i
\(813\) 4.84723 3.05427i 0.170000 0.107118i
\(814\) −27.7438 48.0537i −0.972421 1.68428i
\(815\) −12.2130 −0.427803
\(816\) 52.3643 2.02563i 1.83312 0.0709114i
\(817\) 20.7274i 0.725160i
\(818\) 11.5814 0.404933
\(819\) −14.0631 1.65231i −0.491405 0.0577363i
\(820\) 14.2065 0.496114
\(821\) 12.7579i 0.445254i 0.974904 + 0.222627i \(0.0714632\pi\)
−0.974904 + 0.222627i \(0.928537\pi\)
\(822\) −1.12361 1.78320i −0.0391902 0.0621962i
\(823\) −36.3966 −1.26871 −0.634353 0.773043i \(-0.718733\pi\)
−0.634353 + 0.773043i \(0.718733\pi\)
\(824\) 32.1023 + 55.6028i 1.11834 + 1.93701i
\(825\) 0.293417 + 7.58507i 0.0102155 + 0.264078i
\(826\) 56.6557 + 11.1479i 1.97130 + 0.387886i
\(827\) 14.5352i 0.505439i −0.967540 0.252720i \(-0.918675\pi\)
0.967540 0.252720i \(-0.0813250\pi\)
\(828\) −24.4031 11.6760i −0.848068 0.405769i
\(829\) 2.33693 1.34923i 0.0811651 0.0468607i −0.458868 0.888504i \(-0.651745\pi\)
0.540033 + 0.841644i \(0.318412\pi\)
\(830\) 13.1020 + 7.56447i 0.454778 + 0.262566i
\(831\) −23.6098 37.4695i −0.819015 1.29980i
\(832\) 12.8183 + 7.40067i 0.444396 + 0.256572i
\(833\) −7.40595 54.5130i −0.256601 1.88876i
\(834\) 25.4803 + 40.4381i 0.882311 + 1.40026i
\(835\) 16.3262 0.564993
\(836\) 33.5870 + 58.1744i 1.16163 + 2.01200i
\(837\) 4.25731 + 36.5385i 0.147154 + 1.26296i
\(838\) 0.508902 + 0.293815i 0.0175797 + 0.0101497i
\(839\) −10.6019 18.3631i −0.366019 0.633964i 0.622920 0.782286i \(-0.285946\pi\)
−0.988939 + 0.148322i \(0.952613\pi\)
\(840\) −21.8537 3.42860i −0.754025 0.118298i
\(841\) −14.1030 + 24.4271i −0.486309 + 0.842312i
\(842\) 26.3827 15.2321i 0.909208 0.524931i
\(843\) −0.436897 11.2941i −0.0150475 0.388991i
\(844\) −30.9837 + 53.6654i −1.06650 + 1.84724i
\(845\) −4.90872 + 8.50215i −0.168865 + 0.292483i
\(846\) −3.62825 + 2.48716i −0.124742 + 0.0855104i
\(847\) 20.5455 7.02162i 0.705953 0.241266i
\(848\) 45.8497 26.4713i 1.57449 0.909029i
\(849\) 7.19129 + 3.78908i 0.246804 + 0.130041i
\(850\) 19.2104i 0.658912i
\(851\) 11.7511i 0.402821i
\(852\) −2.09518 1.10395i −0.0717797 0.0378206i
\(853\) −4.49048 + 2.59258i −0.153751 + 0.0887682i −0.574902 0.818222i \(-0.694960\pi\)
0.421151 + 0.906991i \(0.361626\pi\)
\(854\) 5.42409 27.5661i 0.185608 0.943293i
\(855\) 9.54188 6.54095i 0.326325 0.223696i
\(856\) −46.9121 + 81.2542i −1.60342 + 2.77721i
\(857\) −25.3909 + 43.9783i −0.867337 + 1.50227i −0.00262895 + 0.999997i \(0.500837\pi\)
−0.864708 + 0.502275i \(0.832497\pi\)
\(858\) −1.27949 33.0759i −0.0436811 1.12919i
\(859\) 30.4118 17.5583i 1.03764 0.599080i 0.118474 0.992957i \(-0.462200\pi\)
0.919163 + 0.393877i \(0.128866\pi\)
\(860\) −10.6826 + 18.5028i −0.364273 + 0.630940i
\(861\) −15.2822 + 5.89189i −0.520816 + 0.200795i
\(862\) −2.42658 4.20296i −0.0826497 0.143153i
\(863\) −45.8409 26.4663i −1.56044 0.900922i −0.997212 0.0746216i \(-0.976225\pi\)
−0.563230 0.826300i \(-0.690442\pi\)
\(864\) −0.146992 1.26156i −0.00500076 0.0429192i
\(865\) −2.24985 3.89686i −0.0764973 0.132497i
\(866\) 77.6984 2.64030
\(867\) 41.3348 + 65.5998i 1.40380 + 2.22788i
\(868\) 73.0495 + 14.3737i 2.47946 + 0.487875i
\(869\) 26.0925 + 15.0645i 0.885127 + 0.511028i
\(870\) 2.01123 + 3.19188i 0.0681870 + 0.108215i
\(871\) −10.0225 5.78647i −0.339598 0.196067i
\(872\) −37.7292 + 21.7830i −1.27767 + 0.737665i
\(873\) 32.2166 + 15.4144i 1.09037 + 0.521700i
\(874\) 21.3840i 0.723324i
\(875\) 0.510801 2.59597i 0.0172682 0.0877599i
\(876\) −1.04149 26.9234i −0.0351888 0.909658i
\(877\) 9.65302 + 16.7195i 0.325959 + 0.564578i 0.981706 0.190403i \(-0.0609795\pi\)
−0.655747 + 0.754981i \(0.727646\pi\)
\(878\) 18.0127 0.607900
\(879\) 9.73474 + 15.4493i 0.328344 + 0.521094i
\(880\) 16.8713i 0.568732i
\(881\) −0.474565 −0.0159885 −0.00799424 0.999968i \(-0.502545\pi\)
−0.00799424 + 0.999968i \(0.502545\pi\)
\(882\) 50.1783 10.8189i 1.68959 0.364291i
\(883\) −43.6911 −1.47032 −0.735162 0.677892i \(-0.762894\pi\)
−0.735162 + 0.677892i \(0.762894\pi\)
\(884\) 55.7291i 1.87437i
\(885\) 15.4531 0.597780i 0.519450 0.0200942i
\(886\) −100.567 −3.37860
\(887\) −13.9301 24.1276i −0.467726 0.810125i 0.531594 0.846999i \(-0.321593\pi\)
−0.999320 + 0.0368743i \(0.988260\pi\)
\(888\) 36.6406 23.0875i 1.22958 0.774765i
\(889\) 1.61660 8.21585i 0.0542192 0.275551i
\(890\) 8.26282i 0.276970i
\(891\) −30.7127 + 24.7477i −1.02892 + 0.829080i
\(892\) 11.6095 6.70276i 0.388716 0.224425i
\(893\) −2.00330 1.15661i −0.0670380 0.0387044i
\(894\) 47.6510 1.84331i 1.59369 0.0616495i
\(895\) −7.40489 4.27521i −0.247518 0.142905i
\(896\) −51.3783 10.1095i −1.71643 0.337736i
\(897\) −3.26770 + 6.20177i −0.109105 + 0.207071i
\(898\) 63.5943 2.12217
\(899\) −3.15423 5.46329i −0.105200 0.182211i
\(900\) −11.8889 + 0.921187i −0.396296 + 0.0307062i
\(901\) 93.6019 + 54.0411i 3.11833 + 1.80037i
\(902\) −19.1437 33.1578i −0.637414 1.10403i
\(903\) 3.81776 24.3342i 0.127047 0.809790i
\(904\) −31.7809 + 55.0461i −1.05702 + 1.83081i
\(905\) 0.755935 0.436440i 0.0251281 0.0145077i
\(906\) −8.36125 + 5.26848i −0.277784 + 0.175033i
\(907\) 2.13062 3.69034i 0.0707461 0.122536i −0.828482 0.560015i \(-0.810795\pi\)
0.899229 + 0.437479i \(0.144129\pi\)
\(908\) −38.4935 + 66.6727i −1.27745 + 2.21261i
\(909\) 50.4127 3.90613i 1.67208 0.129558i
\(910\) −2.22742 + 11.3201i −0.0738384 + 0.375259i
\(911\) 3.52078 2.03273i 0.116649 0.0673472i −0.440540 0.897733i \(-0.645213\pi\)
0.557189 + 0.830386i \(0.311880\pi\)
\(912\) −21.7541 + 13.7074i −0.720349 + 0.453897i
\(913\) 27.1249i 0.897704i
\(914\) 75.0728i 2.48319i
\(915\) −0.290853 7.51879i −0.00961531 0.248563i
\(916\) −36.0475 + 20.8120i −1.19104 + 0.687649i
\(917\) −14.7276 + 5.03330i −0.486349 + 0.166214i
\(918\) −80.0898 + 59.5795i −2.64336 + 1.96642i
\(919\) 11.2988 19.5700i 0.372712 0.645556i −0.617270 0.786751i \(-0.711761\pi\)
0.989982 + 0.141196i \(0.0450947\pi\)
\(920\) −5.47562 + 9.48405i −0.180526 + 0.312680i
\(921\) −19.8623 10.4654i −0.654484 0.344847i
\(922\) −66.7974 + 38.5655i −2.19986 + 1.27009i
\(923\) −0.306832 + 0.531448i −0.0100995 + 0.0174928i
\(924\) 28.7164 + 74.4837i 0.944700 + 2.45033i
\(925\) 2.58988 + 4.48580i 0.0851547 + 0.147492i
\(926\) 51.8568 + 29.9395i 1.70412 + 0.983874i
\(927\) −35.9938 17.2217i −1.18219 0.565636i
\(928\) 0.108906 + 0.188631i 0.00357501 + 0.00619210i
\(929\) −4.91016 −0.161097 −0.0805486 0.996751i \(-0.525667\pi\)
−0.0805486 + 0.996751i \(0.525667\pi\)
\(930\) 29.9500 1.15857i 0.982098 0.0379910i
\(931\) 16.5208 + 21.3472i 0.541447 + 0.699625i
\(932\) −43.5832 25.1628i −1.42762 0.824234i
\(933\) −9.14712 + 17.3603i −0.299463 + 0.568350i
\(934\) −5.65635 3.26570i −0.185082 0.106857i
\(935\) 29.8283 17.2214i 0.975488 0.563198i
\(936\) 25.7576 1.99578i 0.841913 0.0652340i
\(937\) 53.9957i 1.76396i −0.471284 0.881982i \(-0.656209\pi\)
0.471284 0.881982i \(-0.343791\pi\)
\(938\) 41.1641 + 8.09972i 1.34406 + 0.264465i
\(939\) −7.77396 4.09609i −0.253694 0.133671i
\(940\) 1.19220 + 2.06495i 0.0388852 + 0.0673511i
\(941\) 7.27482 0.237152 0.118576 0.992945i \(-0.462167\pi\)
0.118576 + 0.992945i \(0.462167\pi\)
\(942\) 47.3865 89.9348i 1.54394 2.93023i
\(943\) 8.10841i 0.264046i
\(944\) −34.3720 −1.11871
\(945\) 12.4070 5.92163i 0.403601 0.192631i
\(946\) 57.5803 1.87210
\(947\) 24.4635i 0.794957i 0.917612 + 0.397478i \(0.130115\pi\)
−0.917612 + 0.397478i \(0.869885\pi\)
\(948\) −22.0632 + 41.8736i −0.716578 + 1.35999i
\(949\) −6.98173 −0.226636
\(950\) −4.71293 8.16304i −0.152908 0.264844i
\(951\) 15.2814 + 8.05178i 0.495535 + 0.261097i
\(952\) 32.4601 + 94.9797i 1.05204 + 3.07831i
\(953\) 24.1698i 0.782938i 0.920191 + 0.391469i \(0.128033\pi\)
−0.920191 + 0.391469i \(0.871967\pi\)
\(954\) −43.5262 + 90.9708i −1.40921 + 2.94529i
\(955\) 13.4463 7.76320i 0.435111 0.251211i
\(956\) −67.4970 38.9694i −2.18301 1.26036i
\(957\) 3.15310 5.98425i 0.101925 0.193443i
\(958\) 7.56075 + 4.36520i 0.244277 + 0.141033i
\(959\) 0.866397 0.992062i 0.0279774 0.0320353i
\(960\) −14.3598 + 0.555488i −0.463461 + 0.0179283i
\(961\) −19.1180 −0.616710
\(962\) −11.2936 19.5610i −0.364119 0.630673i
\(963\) −4.50451 58.1354i −0.145156 1.87339i
\(964\) 6.05343 + 3.49495i 0.194968 + 0.112565i
\(965\) 5.25698 + 9.10536i 0.169228 + 0.293112i
\(966\) 3.93870 25.1050i 0.126725 0.807741i
\(967\) −1.86561 + 3.23133i −0.0599939 + 0.103913i −0.894462 0.447143i \(-0.852441\pi\)
0.834469 + 0.551056i \(0.185775\pi\)
\(968\) −34.3070 + 19.8071i −1.10267 + 0.636625i
\(969\) −46.4398 24.4691i −1.49186 0.786061i
\(970\) 14.5497 25.2008i 0.467163 0.809150i
\(971\) −20.5327 + 35.5637i −0.658926 + 1.14129i 0.321968 + 0.946751i \(0.395656\pi\)
−0.980894 + 0.194543i \(0.937678\pi\)
\(972\) −40.7129 46.7087i −1.30587 1.49818i
\(973\) −19.6475 + 22.4973i −0.629871 + 0.721229i
\(974\) −34.6186 + 19.9871i −1.10925 + 0.640426i
\(975\) 0.119440 + 3.08762i 0.00382514 + 0.0988830i
\(976\) 16.7239i 0.535319i
\(977\) 48.1446i 1.54028i −0.637874 0.770141i \(-0.720186\pi\)
0.637874 0.770141i \(-0.279814\pi\)
\(978\) −43.7465 + 27.5650i −1.39886 + 0.881430i
\(979\) −12.8298 + 7.40728i −0.410042 + 0.236738i
\(980\) −3.74565 27.5706i −0.119650 0.880711i
\(981\) 11.6858 24.4236i 0.373099 0.779786i
\(982\) −51.2615 + 88.7875i −1.63582 + 2.83332i
\(983\) −2.82493 + 4.89292i −0.0901013 + 0.156060i −0.907554 0.419936i \(-0.862052\pi\)
0.817452 + 0.575996i \(0.195386\pi\)
\(984\) 25.2825 15.9307i 0.805978 0.507852i
\(985\) 5.35485 3.09162i 0.170620 0.0985073i
\(986\) 8.55921 14.8250i 0.272581 0.472124i
\(987\) −2.13886 1.72685i −0.0680807 0.0549664i
\(988\) 13.6721 + 23.6808i 0.434968 + 0.753387i
\(989\) −10.5605 6.09712i −0.335805 0.193877i
\(990\) 18.1706 + 26.5071i 0.577500 + 0.842452i
\(991\) −12.8768 22.3033i −0.409046 0.708489i 0.585737 0.810501i \(-0.300805\pi\)
−0.994783 + 0.102013i \(0.967472\pi\)
\(992\) 1.73042 0.0549409
\(993\) −20.2007 + 38.3389i −0.641051 + 1.21665i
\(994\) 0.429494 2.18276i 0.0136227 0.0692329i
\(995\) −11.5085 6.64441i −0.364843 0.210642i
\(996\) 42.5795 1.64713i 1.34918 0.0521912i
\(997\) −25.7278 14.8540i −0.814809 0.470430i 0.0338142 0.999428i \(-0.489235\pi\)
−0.848623 + 0.528998i \(0.822568\pi\)
\(998\) 65.7972 37.9880i 2.08277 1.20249i
\(999\) −10.6694 + 24.7098i −0.337564 + 0.781782i
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 315.2.t.c.131.2 yes 32
3.2 odd 2 945.2.t.c.341.15 32
7.3 odd 6 315.2.be.c.311.15 yes 32
9.2 odd 6 315.2.be.c.236.15 yes 32
9.7 even 3 945.2.be.c.656.2 32
21.17 even 6 945.2.be.c.206.2 32
63.38 even 6 inner 315.2.t.c.101.15 32
63.52 odd 6 945.2.t.c.521.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.t.c.101.15 32 63.38 even 6 inner
315.2.t.c.131.2 yes 32 1.1 even 1 trivial
315.2.be.c.236.15 yes 32 9.2 odd 6
315.2.be.c.311.15 yes 32 7.3 odd 6
945.2.t.c.341.15 32 3.2 odd 2
945.2.t.c.521.2 32 63.52 odd 6
945.2.be.c.206.2 32 21.17 even 6
945.2.be.c.656.2 32 9.7 even 3