Properties

Label 392.2.bc.a.299.18
Level $392$
Weight $2$
Character 392.299
Analytic conductor $3.130$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,2,Mod(3,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 21, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 392.bc (of order \(42\), degree \(12\), 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: \(3.13013575923\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 299.18
Character \(\chi\) \(=\) 392.299
Dual form 392.2.bc.a.59.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.722295 - 1.21585i) q^{2} +(0.240470 - 0.352705i) q^{3} +(-0.956578 + 1.75640i) q^{4} +(0.0287133 - 0.383153i) q^{5} +(-0.602526 - 0.0376182i) q^{6} +(-1.65055 + 2.06778i) q^{7} +(2.82646 - 0.105588i) q^{8} +(1.02945 + 2.62299i) q^{9} +O(q^{10})\) \(q+(-0.722295 - 1.21585i) q^{2} +(0.240470 - 0.352705i) q^{3} +(-0.956578 + 1.75640i) q^{4} +(0.0287133 - 0.383153i) q^{5} +(-0.602526 - 0.0376182i) q^{6} +(-1.65055 + 2.06778i) q^{7} +(2.82646 - 0.105588i) q^{8} +(1.02945 + 2.62299i) q^{9} +(-0.486596 + 0.241838i) q^{10} +(1.87657 - 4.78142i) q^{11} +(0.389464 + 0.759753i) q^{12} +(3.05438 + 3.83008i) q^{13} +(3.70629 + 0.513272i) q^{14} +(-0.128235 - 0.102264i) q^{15} +(-2.16992 - 3.36028i) q^{16} +(-1.37239 - 1.47909i) q^{17} +(2.44560 - 3.14623i) q^{18} +(6.59153 + 3.80562i) q^{19} +(0.645505 + 0.416948i) q^{20} +(0.332407 + 1.07939i) q^{21} +(-7.16893 + 1.17197i) q^{22} +(1.43724 - 1.54898i) q^{23} +(0.642437 - 1.02230i) q^{24} +(4.79817 + 0.723208i) q^{25} +(2.45063 - 6.48012i) q^{26} +(2.42122 + 0.552629i) q^{27} +(-2.05297 - 4.87702i) q^{28} +(-1.71969 + 0.392509i) q^{29} +(-0.0317141 + 0.229780i) q^{30} +(-2.79218 - 4.83620i) q^{31} +(-2.51827 + 5.06540i) q^{32} +(-1.23517 - 1.81166i) q^{33} +(-0.807074 + 2.73696i) q^{34} +(0.744881 + 0.691785i) q^{35} +(-5.59178 - 0.700969i) q^{36} +(-1.94614 + 6.30922i) q^{37} +(-0.133971 - 10.7631i) q^{38} +(2.08537 - 0.156277i) q^{39} +(0.0407006 - 1.08600i) q^{40} +(-0.147753 - 0.306812i) q^{41} +(1.07228 - 1.18380i) q^{42} +(1.11584 + 0.537359i) q^{43} +(6.60303 + 7.86982i) q^{44} +(1.03457 - 0.319121i) q^{45} +(-2.92144 - 0.628649i) q^{46} +(6.92682 - 1.04405i) q^{47} +(-1.70699 - 0.0427066i) q^{48} +(-1.55139 - 6.82592i) q^{49} +(-2.58639 - 6.35622i) q^{50} +(-0.851701 + 0.128373i) q^{51} +(-9.64892 + 1.70097i) q^{52} +(0.313014 + 1.01477i) q^{53} +(-1.07693 - 3.34301i) q^{54} +(-1.77813 - 0.856304i) q^{55} +(-4.44687 + 6.01875i) q^{56} +(2.92733 - 1.40973i) q^{57} +(1.71936 + 1.80738i) q^{58} +(-5.81225 + 0.435568i) q^{59} +(0.302284 - 0.127409i) q^{60} +(8.69533 + 2.68215i) q^{61} +(-3.86331 + 6.88804i) q^{62} +(-7.12291 - 2.20070i) q^{63} +(7.97770 - 0.596881i) q^{64} +(1.55521 - 1.06032i) q^{65} +(-1.31055 + 2.81034i) q^{66} +(-6.09551 - 10.5577i) q^{67} +(3.91068 - 0.995614i) q^{68} +(-0.200718 - 0.879405i) q^{69} +(0.303081 - 1.40534i) q^{70} +(-1.21233 - 0.276706i) q^{71} +(3.18665 + 7.30507i) q^{72} +(-1.28872 + 8.55007i) q^{73} +(9.07675 - 2.19091i) q^{74} +(1.40890 - 1.51843i) q^{75} +(-12.9895 + 7.93702i) q^{76} +(6.78954 + 11.7723i) q^{77} +(-1.69627 - 2.42262i) q^{78} +(-12.7347 - 7.35240i) q^{79} +(-1.34981 + 0.734924i) q^{80} +(-5.41958 + 5.02863i) q^{81} +(-0.266316 + 0.401254i) q^{82} +(8.01747 + 6.39372i) q^{83} +(-2.21383 - 0.448684i) q^{84} +(-0.606123 + 0.483367i) q^{85} +(-0.152617 - 1.74482i) q^{86} +(-0.275095 + 0.700931i) q^{87} +(4.79918 - 13.7126i) q^{88} +(-7.52894 + 2.95489i) q^{89} +(-1.13527 - 1.02738i) q^{90} +(-12.9611 - 0.00594332i) q^{91} +(1.34580 + 4.00610i) q^{92} +(-2.37719 - 0.178146i) q^{93} +(-6.27262 - 7.66786i) q^{94} +(1.64740 - 2.41629i) q^{95} +(1.18102 + 2.10628i) q^{96} +1.81367i q^{97} +(-7.17873 + 6.81658i) q^{98} +14.4735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 13 q^{2} - 22 q^{3} - 13 q^{4} - 14 q^{6} - 4 q^{8} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 13 q^{2} - 22 q^{3} - 13 q^{4} - 14 q^{6} - 4 q^{8} - 76 q^{9} - 20 q^{10} - 26 q^{11} - 31 q^{12} + 15 q^{14} - 9 q^{16} - 22 q^{17} - 18 q^{18} - 36 q^{19} - 14 q^{20} - 26 q^{22} + 22 q^{24} + 20 q^{25} - 20 q^{26} - 28 q^{27} - 62 q^{28} - 5 q^{30} - 23 q^{32} - 22 q^{33} - 42 q^{34} - 46 q^{35} - 32 q^{36} - 4 q^{38} - 28 q^{41} + 16 q^{42} - 20 q^{43} + 6 q^{46} - 16 q^{49} - 140 q^{50} - 34 q^{51} + 10 q^{52} + 43 q^{54} + 56 q^{56} - 34 q^{57} - 16 q^{58} - 70 q^{59} + 92 q^{60} + 20 q^{64} - 16 q^{65} + 2 q^{66} - 24 q^{67} + 15 q^{68} - 114 q^{70} + 110 q^{72} - 46 q^{73} - 34 q^{74} - 52 q^{75} - 147 q^{76} + 48 q^{78} + 6 q^{80} + 70 q^{81} - 68 q^{82} - 28 q^{83} + 128 q^{84} - 117 q^{86} + 133 q^{88} - 46 q^{89} - 294 q^{90} - 124 q^{91} - 102 q^{92} - 44 q^{94} + 38 q^{96} - 225 q^{98} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{29}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.722295 1.21585i −0.510740 0.859735i
\(3\) 0.240470 0.352705i 0.138835 0.203634i −0.750524 0.660844i \(-0.770199\pi\)
0.889359 + 0.457209i \(0.151151\pi\)
\(4\) −0.956578 + 1.75640i −0.478289 + 0.878202i
\(5\) 0.0287133 0.383153i 0.0128410 0.171351i −0.987096 0.160129i \(-0.948809\pi\)
0.999937 0.0112218i \(-0.00357209\pi\)
\(6\) −0.602526 0.0376182i −0.245980 0.0153576i
\(7\) −1.65055 + 2.06778i −0.623848 + 0.781545i
\(8\) 2.82646 0.105588i 0.999303 0.0373311i
\(9\) 1.02945 + 2.62299i 0.343149 + 0.874330i
\(10\) −0.486596 + 0.241838i −0.153875 + 0.0764760i
\(11\) 1.87657 4.78142i 0.565807 1.44165i −0.306108 0.951997i \(-0.599027\pi\)
0.871915 0.489657i \(-0.162878\pi\)
\(12\) 0.389464 + 0.759753i 0.112429 + 0.219322i
\(13\) 3.05438 + 3.83008i 0.847133 + 1.06227i 0.997287 + 0.0736091i \(0.0234517\pi\)
−0.150154 + 0.988663i \(0.547977\pi\)
\(14\) 3.70629 + 0.513272i 0.990546 + 0.137178i
\(15\) −0.128235 0.102264i −0.0331102 0.0264045i
\(16\) −2.16992 3.36028i −0.542479 0.840069i
\(17\) −1.37239 1.47909i −0.332854 0.358731i 0.544342 0.838863i \(-0.316779\pi\)
−0.877196 + 0.480132i \(0.840589\pi\)
\(18\) 2.44560 3.14623i 0.576433 0.741573i
\(19\) 6.59153 + 3.80562i 1.51220 + 0.873070i 0.999898 + 0.0142648i \(0.00454078\pi\)
0.512303 + 0.858805i \(0.328793\pi\)
\(20\) 0.645505 + 0.416948i 0.144339 + 0.0932324i
\(21\) 0.332407 + 1.07939i 0.0725371 + 0.235543i
\(22\) −7.16893 + 1.17197i −1.52842 + 0.249866i
\(23\) 1.43724 1.54898i 0.299686 0.322984i −0.565199 0.824954i \(-0.691201\pi\)
0.864885 + 0.501970i \(0.167391\pi\)
\(24\) 0.642437 1.02230i 0.131137 0.208675i
\(25\) 4.79817 + 0.723208i 0.959634 + 0.144642i
\(26\) 2.45063 6.48012i 0.480607 1.27086i
\(27\) 2.42122 + 0.552629i 0.465965 + 0.106353i
\(28\) −2.05297 4.87702i −0.387975 0.921670i
\(29\) −1.71969 + 0.392509i −0.319339 + 0.0728871i −0.379186 0.925320i \(-0.623796\pi\)
0.0598467 + 0.998208i \(0.480939\pi\)
\(30\) −0.0317141 + 0.229780i −0.00579017 + 0.0419518i
\(31\) −2.79218 4.83620i −0.501491 0.868607i −0.999999 0.00172218i \(-0.999452\pi\)
0.498508 0.866885i \(-0.333882\pi\)
\(32\) −2.51827 + 5.06540i −0.445172 + 0.895445i
\(33\) −1.23517 1.81166i −0.215016 0.315370i
\(34\) −0.807074 + 2.73696i −0.138412 + 0.469385i
\(35\) 0.744881 + 0.691785i 0.125908 + 0.116933i
\(36\) −5.59178 0.700969i −0.931964 0.116828i
\(37\) −1.94614 + 6.30922i −0.319943 + 1.03723i 0.642623 + 0.766182i \(0.277846\pi\)
−0.962566 + 0.271047i \(0.912630\pi\)
\(38\) −0.133971 10.7631i −0.0217329 1.74600i
\(39\) 2.08537 0.156277i 0.333927 0.0250244i
\(40\) 0.0407006 1.08600i 0.00643532 0.171711i
\(41\) −0.147753 0.306812i −0.0230751 0.0479159i 0.889113 0.457688i \(-0.151322\pi\)
−0.912188 + 0.409772i \(0.865608\pi\)
\(42\) 1.07228 1.18380i 0.165457 0.182664i
\(43\) 1.11584 + 0.537359i 0.170164 + 0.0819465i 0.517027 0.855969i \(-0.327039\pi\)
−0.346863 + 0.937916i \(0.612753\pi\)
\(44\) 6.60303 + 7.86982i 0.995444 + 1.18642i
\(45\) 1.03457 0.319121i 0.154224 0.0475718i
\(46\) −2.92144 0.628649i −0.430742 0.0926893i
\(47\) 6.92682 1.04405i 1.01038 0.152290i 0.377067 0.926186i \(-0.376932\pi\)
0.633313 + 0.773895i \(0.281694\pi\)
\(48\) −1.70699 0.0427066i −0.246382 0.00616417i
\(49\) −1.55139 6.82592i −0.221627 0.975132i
\(50\) −2.58639 6.35622i −0.365770 0.898906i
\(51\) −0.851701 + 0.128373i −0.119262 + 0.0179758i
\(52\) −9.64892 + 1.70097i −1.33806 + 0.235881i
\(53\) 0.313014 + 1.01477i 0.0429958 + 0.139389i 0.974526 0.224276i \(-0.0720016\pi\)
−0.931530 + 0.363665i \(0.881525\pi\)
\(54\) −1.07693 3.34301i −0.146551 0.454925i
\(55\) −1.77813 0.856304i −0.239763 0.115464i
\(56\) −4.44687 + 6.01875i −0.594237 + 0.804290i
\(57\) 2.92733 1.40973i 0.387734 0.186723i
\(58\) 1.71936 + 1.80738i 0.225763 + 0.237321i
\(59\) −5.81225 + 0.435568i −0.756691 + 0.0567061i −0.447488 0.894290i \(-0.647681\pi\)
−0.309203 + 0.950996i \(0.600062\pi\)
\(60\) 0.302284 0.127409i 0.0390247 0.0164485i
\(61\) 8.69533 + 2.68215i 1.11332 + 0.343415i 0.796239 0.604983i \(-0.206820\pi\)
0.317084 + 0.948397i \(0.397296\pi\)
\(62\) −3.86331 + 6.88804i −0.490641 + 0.874782i
\(63\) −7.12291 2.20070i −0.897402 0.277263i
\(64\) 7.97770 0.596881i 0.997213 0.0746101i
\(65\) 1.55521 1.06032i 0.192900 0.131517i
\(66\) −1.31055 + 2.81034i −0.161318 + 0.345929i
\(67\) −6.09551 10.5577i −0.744685 1.28983i −0.950342 0.311208i \(-0.899266\pi\)
0.205656 0.978624i \(-0.434067\pi\)
\(68\) 3.91068 0.995614i 0.474239 0.120736i
\(69\) −0.200718 0.879405i −0.0241637 0.105868i
\(70\) 0.303081 1.40534i 0.0362252 0.167970i
\(71\) −1.21233 0.276706i −0.143877 0.0328390i 0.149976 0.988690i \(-0.452080\pi\)
−0.293853 + 0.955851i \(0.594938\pi\)
\(72\) 3.18665 + 7.30507i 0.375550 + 0.860911i
\(73\) −1.28872 + 8.55007i −0.150833 + 1.00071i 0.777479 + 0.628909i \(0.216498\pi\)
−0.928312 + 0.371802i \(0.878740\pi\)
\(74\) 9.07675 2.19091i 1.05515 0.254688i
\(75\) 1.40890 1.51843i 0.162685 0.175333i
\(76\) −12.9895 + 7.93702i −1.49000 + 0.910439i
\(77\) 6.78954 + 11.7723i 0.773740 + 1.34158i
\(78\) −1.69627 2.42262i −0.192064 0.274308i
\(79\) −12.7347 7.35240i −1.43277 0.827210i −0.435438 0.900219i \(-0.643406\pi\)
−0.997331 + 0.0730091i \(0.976740\pi\)
\(80\) −1.34981 + 0.734924i −0.150913 + 0.0821671i
\(81\) −5.41958 + 5.02863i −0.602175 + 0.558737i
\(82\) −0.266316 + 0.401254i −0.0294096 + 0.0443111i
\(83\) 8.01747 + 6.39372i 0.880031 + 0.701802i 0.955388 0.295355i \(-0.0954380\pi\)
−0.0753562 + 0.997157i \(0.524009\pi\)
\(84\) −2.21383 0.448684i −0.241548 0.0489554i
\(85\) −0.606123 + 0.483367i −0.0657432 + 0.0524285i
\(86\) −0.152617 1.74482i −0.0164571 0.188149i
\(87\) −0.275095 + 0.700931i −0.0294933 + 0.0751477i
\(88\) 4.79918 13.7126i 0.511594 1.46177i
\(89\) −7.52894 + 2.95489i −0.798066 + 0.313218i −0.729105 0.684402i \(-0.760063\pi\)
−0.0689605 + 0.997619i \(0.521968\pi\)
\(90\) −1.13527 1.02738i −0.119667 0.108295i
\(91\) −12.9611 0.00594332i −1.35870 0.000623030i
\(92\) 1.34580 + 4.00610i 0.140309 + 0.417665i
\(93\) −2.37719 0.178146i −0.246503 0.0184728i
\(94\) −6.27262 7.66786i −0.646971 0.790879i
\(95\) 1.64740 2.41629i 0.169020 0.247906i
\(96\) 1.18102 + 2.10628i 0.120538 + 0.214972i
\(97\) 1.81367i 0.184150i 0.995752 + 0.0920752i \(0.0293500\pi\)
−0.995752 + 0.0920752i \(0.970650\pi\)
\(98\) −7.17873 + 6.81658i −0.725161 + 0.688579i
\(99\) 14.4735 1.45464
\(100\) −5.86007 + 7.73573i −0.586007 + 0.773573i
\(101\) 9.27225 + 6.32171i 0.922623 + 0.629034i 0.928654 0.370948i \(-0.120967\pi\)
−0.00603059 + 0.999982i \(0.501920\pi\)
\(102\) 0.771262 + 0.942816i 0.0763663 + 0.0933527i
\(103\) −0.796115 + 10.6234i −0.0784435 + 1.04676i 0.809596 + 0.586988i \(0.199686\pi\)
−0.888039 + 0.459768i \(0.847933\pi\)
\(104\) 9.03749 + 10.5030i 0.886199 + 1.02991i
\(105\) 0.423117 0.0963697i 0.0412920 0.00940472i
\(106\) 1.00772 1.11354i 0.0978780 0.108157i
\(107\) 2.66334 + 6.78609i 0.257475 + 0.656036i 0.999904 0.0138893i \(-0.00442124\pi\)
−0.742428 + 0.669926i \(0.766326\pi\)
\(108\) −3.28673 + 3.72402i −0.316266 + 0.358344i
\(109\) −1.98386 0.778607i −0.190019 0.0745770i 0.268424 0.963301i \(-0.413497\pi\)
−0.458443 + 0.888724i \(0.651593\pi\)
\(110\) 0.243201 + 2.78045i 0.0231883 + 0.265105i
\(111\) 1.75730 + 2.20359i 0.166796 + 0.209156i
\(112\) 10.5298 + 1.05940i 0.994977 + 0.100104i
\(113\) −9.84621 + 12.3468i −0.926254 + 1.16149i 0.0603219 + 0.998179i \(0.480787\pi\)
−0.986575 + 0.163306i \(0.947784\pi\)
\(114\) −3.82841 2.54095i −0.358563 0.237982i
\(115\) −0.552227 0.595160i −0.0514955 0.0554989i
\(116\) 0.955618 3.39595i 0.0887269 0.315306i
\(117\) −6.90192 + 11.9545i −0.638083 + 1.10519i
\(118\) 4.72775 + 6.75221i 0.435224 + 0.621591i
\(119\) 5.32362 0.396495i 0.488015 0.0363467i
\(120\) −0.373249 0.275505i −0.0340728 0.0251500i
\(121\) −11.2769 10.4635i −1.02517 0.951223i
\(122\) −3.01950 12.5095i −0.273373 1.13256i
\(123\) −0.143744 0.0216659i −0.0129610 0.00195355i
\(124\) 11.1653 0.277996i 1.00267 0.0249648i
\(125\) 0.842364 3.69064i 0.0753433 0.330101i
\(126\) 2.46912 + 10.2499i 0.219967 + 0.913137i
\(127\) 0.122669 0.0279983i 0.0108851 0.00248445i −0.217075 0.976155i \(-0.569652\pi\)
0.227960 + 0.973670i \(0.426794\pi\)
\(128\) −6.48798 9.26856i −0.573461 0.819233i
\(129\) 0.457855 0.264342i 0.0403118 0.0232741i
\(130\) −2.41251 1.12503i −0.211591 0.0986717i
\(131\) −7.61068 11.1628i −0.664948 0.975300i −0.999458 0.0329080i \(-0.989523\pi\)
0.334510 0.942392i \(-0.391429\pi\)
\(132\) 4.36355 0.436463i 0.379799 0.0379892i
\(133\) −18.7488 + 7.34844i −1.62573 + 0.637191i
\(134\) −8.43385 + 15.0370i −0.728574 + 1.29900i
\(135\) 0.281263 0.911831i 0.0242072 0.0784779i
\(136\) −4.03518 4.03567i −0.346014 0.346056i
\(137\) −0.972439 12.9763i −0.0830811 1.10864i −0.870482 0.492200i \(-0.836193\pi\)
0.787401 0.616441i \(-0.211426\pi\)
\(138\) −0.924246 + 0.879234i −0.0786770 + 0.0748453i
\(139\) −0.462513 0.960419i −0.0392299 0.0814617i 0.880433 0.474171i \(-0.157252\pi\)
−0.919663 + 0.392709i \(0.871538\pi\)
\(140\) −1.92759 + 0.646567i −0.162911 + 0.0546448i
\(141\) 1.29745 2.69419i 0.109265 0.226891i
\(142\) 0.539227 + 1.67387i 0.0452509 + 0.140468i
\(143\) 24.0450 7.41689i 2.01074 0.620232i
\(144\) 6.58016 9.15090i 0.548347 0.762575i
\(145\) 0.101013 + 0.670176i 0.00838866 + 0.0556551i
\(146\) 11.3264 4.60879i 0.937382 0.381427i
\(147\) −2.78060 1.09425i −0.229340 0.0902521i
\(148\) −9.21991 9.45347i −0.757872 0.777070i
\(149\) −3.38853 22.4814i −0.277599 1.84175i −0.499045 0.866576i \(-0.666316\pi\)
0.221446 0.975173i \(-0.428922\pi\)
\(150\) −2.86382 0.616251i −0.233830 0.0503167i
\(151\) −6.70461 21.7358i −0.545613 1.76883i −0.634643 0.772805i \(-0.718853\pi\)
0.0890300 0.996029i \(-0.471623\pi\)
\(152\) 19.0325 + 10.0604i 1.54374 + 0.816009i
\(153\) 2.46683 5.12242i 0.199431 0.414123i
\(154\) 9.40928 16.7581i 0.758221 1.35041i
\(155\) −1.93318 + 0.930969i −0.155277 + 0.0747772i
\(156\) −1.72034 + 3.81225i −0.137737 + 0.305224i
\(157\) −1.07308 14.3193i −0.0856412 1.14280i −0.860082 0.510156i \(-0.829588\pi\)
0.774441 0.632646i \(-0.218031\pi\)
\(158\) 0.258829 + 20.7941i 0.0205913 + 1.65429i
\(159\) 0.433184 + 0.133620i 0.0343537 + 0.0105967i
\(160\) 1.86852 + 1.11033i 0.147719 + 0.0877791i
\(161\) 0.830703 + 5.52855i 0.0654686 + 0.435711i
\(162\) 10.0286 + 2.95723i 0.787921 + 0.232342i
\(163\) 4.18225 2.85141i 0.327579 0.223340i −0.388351 0.921512i \(-0.626955\pi\)
0.715930 + 0.698172i \(0.246003\pi\)
\(164\) 0.680223 + 0.0339759i 0.0531165 + 0.00265307i
\(165\) −0.729610 + 0.421241i −0.0568001 + 0.0327935i
\(166\) 1.98281 14.3662i 0.153896 1.11503i
\(167\) −4.85062 21.2519i −0.375352 1.64452i −0.711479 0.702707i \(-0.751974\pi\)
0.336127 0.941817i \(-0.390883\pi\)
\(168\) 1.05350 + 3.01576i 0.0812797 + 0.232671i
\(169\) −2.44745 + 10.7230i −0.188265 + 0.824844i
\(170\) 1.02550 + 0.387820i 0.0786523 + 0.0297444i
\(171\) −3.19647 + 21.2072i −0.244441 + 1.62176i
\(172\) −2.01121 + 1.44584i −0.153353 + 0.110244i
\(173\) 4.82824 + 4.47995i 0.367084 + 0.340604i 0.842050 0.539400i \(-0.181349\pi\)
−0.474965 + 0.880005i \(0.657539\pi\)
\(174\) 1.05093 0.171805i 0.0796705 0.0130245i
\(175\) −9.41504 + 8.72785i −0.711710 + 0.659764i
\(176\) −20.1389 + 4.06949i −1.51803 + 0.306749i
\(177\) −1.24405 + 2.15475i −0.0935082 + 0.161961i
\(178\) 9.03082 + 7.01975i 0.676888 + 0.526152i
\(179\) 5.95510 5.52552i 0.445105 0.412997i −0.425517 0.904951i \(-0.639908\pi\)
0.870621 + 0.491954i \(0.163717\pi\)
\(180\) −0.429137 + 2.12238i −0.0319860 + 0.158193i
\(181\) 6.36945 7.98704i 0.473437 0.593672i −0.486572 0.873641i \(-0.661753\pi\)
0.960009 + 0.279969i \(0.0903242\pi\)
\(182\) 9.35455 + 15.7631i 0.693405 + 1.16844i
\(183\) 3.03697 2.42191i 0.224500 0.179032i
\(184\) 3.89875 4.52987i 0.287419 0.333947i
\(185\) 2.36152 + 0.926826i 0.173622 + 0.0681416i
\(186\) 1.50043 + 3.01898i 0.110017 + 0.221362i
\(187\) −9.64754 + 3.78638i −0.705498 + 0.276887i
\(188\) −4.79227 + 13.1650i −0.349513 + 0.960158i
\(189\) −5.13906 + 4.09441i −0.373811 + 0.297824i
\(190\) −4.12776 0.257713i −0.299459 0.0186965i
\(191\) −18.3992 1.37883i −1.33132 0.0997684i −0.610016 0.792389i \(-0.708837\pi\)
−0.721302 + 0.692621i \(0.756456\pi\)
\(192\) 1.70788 2.95731i 0.123255 0.213425i
\(193\) 10.2304 + 6.97500i 0.736404 + 0.502072i 0.872494 0.488625i \(-0.162501\pi\)
−0.136090 + 0.990696i \(0.543454\pi\)
\(194\) 2.20515 1.31001i 0.158321 0.0940530i
\(195\) 0.803504i 0.0575401i
\(196\) 13.4731 + 3.80467i 0.962365 + 0.271762i
\(197\) 9.18980i 0.654746i −0.944895 0.327373i \(-0.893837\pi\)
0.944895 0.327373i \(-0.106163\pi\)
\(198\) −10.4541 17.5975i −0.742942 1.25060i
\(199\) −5.48695 3.74094i −0.388959 0.265188i 0.353013 0.935618i \(-0.385157\pi\)
−0.741972 + 0.670430i \(0.766109\pi\)
\(200\) 13.6382 + 1.53749i 0.964365 + 0.108717i
\(201\) −5.18955 0.388903i −0.366043 0.0274311i
\(202\) 0.988945 15.8398i 0.0695819 1.11448i
\(203\) 2.02682 4.20380i 0.142255 0.295049i
\(204\) 0.589243 1.61873i 0.0412553 0.113334i
\(205\) −0.121798 + 0.0478023i −0.00850676 + 0.00333866i
\(206\) 13.4915 6.70529i 0.939997 0.467179i
\(207\) 5.54252 + 2.17528i 0.385232 + 0.151192i
\(208\) 6.24236 18.5745i 0.432830 1.28791i
\(209\) 30.5658 24.3754i 2.11428 1.68608i
\(210\) −0.422787 0.444840i −0.0291751 0.0306968i
\(211\) 3.67990 4.61445i 0.253335 0.317672i −0.638860 0.769323i \(-0.720594\pi\)
0.892194 + 0.451651i \(0.149165\pi\)
\(212\) −2.08177 0.420925i −0.142976 0.0289092i
\(213\) −0.389124 + 0.361055i −0.0266624 + 0.0247391i
\(214\) 6.32714 8.13979i 0.432515 0.556425i
\(215\) 0.237930 0.412107i 0.0162267 0.0281055i
\(216\) 6.90184 + 1.30633i 0.469610 + 0.0888844i
\(217\) 14.6088 + 2.20877i 0.991710 + 0.149941i
\(218\) 0.486263 + 2.97446i 0.0329339 + 0.201456i
\(219\) 2.70575 + 2.51057i 0.182838 + 0.169649i
\(220\) 3.20494 2.30400i 0.216077 0.155336i
\(221\) 1.47320 9.77407i 0.0990984 0.657475i
\(222\) 1.40994 3.72826i 0.0946290 0.250224i
\(223\) −5.75980 + 25.2353i −0.385705 + 1.68988i 0.293520 + 0.955953i \(0.405173\pi\)
−0.679225 + 0.733930i \(0.737684\pi\)
\(224\) −6.31759 13.5679i −0.422112 0.906544i
\(225\) 3.04250 + 13.3301i 0.202833 + 0.888671i
\(226\) 22.1237 + 3.05350i 1.47164 + 0.203116i
\(227\) −9.36752 + 5.40834i −0.621744 + 0.358964i −0.777548 0.628824i \(-0.783537\pi\)
0.155803 + 0.987788i \(0.450203\pi\)
\(228\) −0.324168 + 6.49009i −0.0214685 + 0.429816i
\(229\) 21.1395 14.4127i 1.39694 0.952417i 0.397546 0.917582i \(-0.369862\pi\)
0.999393 0.0348345i \(-0.0110904\pi\)
\(230\) −0.324753 + 1.10131i −0.0214136 + 0.0726180i
\(231\) 5.78482 + 0.436180i 0.380613 + 0.0286986i
\(232\) −4.81920 + 1.29099i −0.316396 + 0.0847576i
\(233\) −27.6148 8.51805i −1.80911 0.558036i −0.809530 0.587079i \(-0.800278\pi\)
−0.999578 + 0.0290431i \(0.990754\pi\)
\(234\) 19.5201 0.242971i 1.27607 0.0158835i
\(235\) −0.201139 2.68401i −0.0131208 0.175086i
\(236\) 4.79484 10.6253i 0.312117 0.691649i
\(237\) −5.65555 + 2.72357i −0.367367 + 0.176915i
\(238\) −4.32731 6.18633i −0.280498 0.401000i
\(239\) 5.27589 10.9555i 0.341269 0.708652i −0.657736 0.753248i \(-0.728486\pi\)
0.999005 + 0.0445962i \(0.0142001\pi\)
\(240\) −0.0653764 + 0.652810i −0.00422003 + 0.0421387i
\(241\) −3.60944 11.7015i −0.232504 0.753760i −0.994364 0.106019i \(-0.966190\pi\)
0.761860 0.647742i \(-0.224286\pi\)
\(242\) −4.57671 + 21.2687i −0.294202 + 1.36721i
\(243\) 1.58081 + 10.4880i 0.101409 + 0.672806i
\(244\) −13.0287 + 12.7068i −0.834078 + 0.813471i
\(245\) −2.65992 + 0.398423i −0.169936 + 0.0254543i
\(246\) 0.0774832 + 0.190420i 0.00494015 + 0.0121408i
\(247\) 5.55724 + 36.8699i 0.353599 + 2.34597i
\(248\) −8.40262 13.3745i −0.533567 0.849281i
\(249\) 4.18306 1.29030i 0.265090 0.0817695i
\(250\) −5.09569 + 1.64154i −0.322280 + 0.103820i
\(251\) −10.8295 + 22.4878i −0.683554 + 1.41942i 0.213254 + 0.976997i \(0.431594\pi\)
−0.896809 + 0.442419i \(0.854121\pi\)
\(252\) 10.6789 10.4056i 0.672710 0.655489i
\(253\) −4.70924 9.77883i −0.296067 0.614790i
\(254\) −0.122645 0.128924i −0.00769542 0.00808938i
\(255\) 0.0247314 + 0.330018i 0.00154874 + 0.0206665i
\(256\) −6.58293 + 14.5830i −0.411433 + 0.911440i
\(257\) −5.46203 + 17.7075i −0.340712 + 1.10456i 0.609455 + 0.792821i \(0.291388\pi\)
−0.950167 + 0.311741i \(0.899088\pi\)
\(258\) −0.652107 0.365749i −0.0405984 0.0227705i
\(259\) −9.83386 14.4378i −0.611046 0.897124i
\(260\) 0.374677 + 3.74585i 0.0232365 + 0.232308i
\(261\) −2.79988 4.10668i −0.173308 0.254197i
\(262\) −8.07515 + 17.3163i −0.498884 + 1.06980i
\(263\) −2.16494 + 1.24993i −0.133496 + 0.0770738i −0.565261 0.824912i \(-0.691224\pi\)
0.431765 + 0.901986i \(0.357891\pi\)
\(264\) −3.68245 4.99017i −0.226639 0.307124i
\(265\) 0.397799 0.0907950i 0.0244366 0.00557749i
\(266\) 22.4768 + 17.4880i 1.37814 + 1.07226i
\(267\) −0.768280 + 3.36605i −0.0470180 + 0.205999i
\(268\) 24.3745 0.606883i 1.48891 0.0370713i
\(269\) −1.47755 0.222704i −0.0900875 0.0135785i 0.103844 0.994594i \(-0.466886\pi\)
−0.193931 + 0.981015i \(0.562124\pi\)
\(270\) −1.31180 + 0.316639i −0.0798339 + 0.0192700i
\(271\) 11.3679 + 10.5479i 0.690551 + 0.640738i 0.945274 0.326276i \(-0.105794\pi\)
−0.254724 + 0.967014i \(0.581984\pi\)
\(272\) −1.99217 + 7.82112i −0.120793 + 0.474225i
\(273\) −3.11886 + 4.57003i −0.188762 + 0.276591i
\(274\) −15.0748 + 10.5551i −0.910704 + 0.637655i
\(275\) 12.4621 21.5849i 0.751491 1.30162i
\(276\) 1.73659 + 0.488677i 0.104531 + 0.0294149i
\(277\) −6.97315 7.51527i −0.418976 0.451549i 0.487929 0.872883i \(-0.337752\pi\)
−0.906905 + 0.421334i \(0.861562\pi\)
\(278\) −0.833653 + 1.25605i −0.0499992 + 0.0753330i
\(279\) 9.81091 12.3025i 0.587364 0.736531i
\(280\) 2.17842 + 1.87665i 0.130185 + 0.112151i
\(281\) −0.171508 0.215065i −0.0102313 0.0128297i 0.776689 0.629884i \(-0.216897\pi\)
−0.786921 + 0.617054i \(0.788326\pi\)
\(282\) −4.21287 + 0.368493i −0.250873 + 0.0219434i
\(283\) −9.77234 3.83536i −0.580905 0.227989i 0.0566487 0.998394i \(-0.481958\pi\)
−0.637554 + 0.770406i \(0.720054\pi\)
\(284\) 1.64570 1.86465i 0.0976541 0.110647i
\(285\) −0.456087 1.16209i −0.0270163 0.0688364i
\(286\) −26.3854 23.8779i −1.56020 1.41193i
\(287\) 0.878291 + 0.200888i 0.0518439 + 0.0118580i
\(288\) −15.8789 1.39083i −0.935675 0.0819556i
\(289\) 0.966173 12.8927i 0.0568337 0.758393i
\(290\) 0.741872 0.606881i 0.0435642 0.0356373i
\(291\) 0.639690 + 0.436134i 0.0374993 + 0.0255666i
\(292\) −13.7846 10.4423i −0.806685 0.611091i
\(293\) 17.2065 1.00522 0.502608 0.864515i \(-0.332374\pi\)
0.502608 + 0.864515i \(0.332374\pi\)
\(294\) 0.677972 + 4.17116i 0.0395402 + 0.243267i
\(295\) 2.23949i 0.130388i
\(296\) −4.83449 + 18.0382i −0.280999 + 1.04845i
\(297\) 7.18595 10.5399i 0.416971 0.611584i
\(298\) −24.8865 + 20.3582i −1.44164 + 1.17932i
\(299\) 10.3226 + 0.773571i 0.596971 + 0.0447368i
\(300\) 1.31926 + 3.92709i 0.0761673 + 0.226730i
\(301\) −2.95288 + 1.42036i −0.170201 + 0.0818684i
\(302\) −21.5847 + 23.8515i −1.24206 + 1.37250i
\(303\) 4.45940 1.75018i 0.256186 0.100545i
\(304\) −1.51512 30.4073i −0.0868979 1.74398i
\(305\) 1.27735 3.25463i 0.0731407 0.186359i
\(306\) −8.00987 + 0.700611i −0.457894 + 0.0400512i
\(307\) 3.63045 2.89519i 0.207201 0.165237i −0.514391 0.857556i \(-0.671982\pi\)
0.721592 + 0.692318i \(0.243411\pi\)
\(308\) −27.1716 + 0.664060i −1.54825 + 0.0378383i
\(309\) 3.55549 + 2.83541i 0.202265 + 0.161301i
\(310\) 2.52824 + 1.67802i 0.143595 + 0.0953050i
\(311\) −15.5752 + 14.4517i −0.883190 + 0.819480i −0.984502 0.175374i \(-0.943886\pi\)
0.101312 + 0.994855i \(0.467696\pi\)
\(312\) 5.87771 0.661901i 0.332760 0.0374728i
\(313\) −17.3612 10.0235i −0.981314 0.566562i −0.0786471 0.996903i \(-0.525060\pi\)
−0.902666 + 0.430341i \(0.858393\pi\)
\(314\) −16.6350 + 11.6474i −0.938767 + 0.657303i
\(315\) −1.04773 + 2.66597i −0.0590328 + 0.150211i
\(316\) 25.0956 15.3342i 1.41174 0.862616i
\(317\) −8.52667 + 9.18956i −0.478905 + 0.516137i −0.925576 0.378561i \(-0.876419\pi\)
0.446671 + 0.894698i \(0.352610\pi\)
\(318\) −0.150426 0.623199i −0.00843545 0.0349473i
\(319\) −1.35038 + 8.95916i −0.0756065 + 0.501617i
\(320\) 0.000369973 3.07382i 2.06821e−5 0.171832i
\(321\) 3.03394 + 0.692477i 0.169338 + 0.0386503i
\(322\) 6.12188 5.00326i 0.341159 0.278821i
\(323\) −3.41732 14.9723i −0.190145 0.833079i
\(324\) −3.64806 14.3292i −0.202670 0.796069i
\(325\) 11.8855 + 20.5863i 0.659290 + 1.14192i
\(326\) −6.48771 3.02543i −0.359321 0.167563i
\(327\) −0.751677 + 0.512485i −0.0415678 + 0.0283405i
\(328\) −0.450012 0.851589i −0.0248478 0.0470211i
\(329\) −9.27419 + 16.0464i −0.511302 + 0.884665i
\(330\) 1.03916 + 0.582836i 0.0572038 + 0.0320841i
\(331\) 8.26955 + 2.55082i 0.454535 + 0.140206i 0.513565 0.858051i \(-0.328324\pi\)
−0.0590297 + 0.998256i \(0.518801\pi\)
\(332\) −18.8993 + 7.96583i −1.03723 + 0.437182i
\(333\) −18.5525 + 1.39032i −1.01667 + 0.0761888i
\(334\) −22.3356 + 21.2478i −1.22215 + 1.16263i
\(335\) −4.22025 + 2.03236i −0.230577 + 0.111040i
\(336\) 2.90577 3.45917i 0.158523 0.188713i
\(337\) 8.20702 + 3.95229i 0.447065 + 0.215295i 0.643850 0.765151i \(-0.277336\pi\)
−0.196785 + 0.980447i \(0.563050\pi\)
\(338\) 14.8053 4.76943i 0.805302 0.259423i
\(339\) 1.98704 + 6.44183i 0.107921 + 0.349872i
\(340\) −0.269184 1.52697i −0.0145985 0.0828118i
\(341\) −28.3637 + 4.27513i −1.53598 + 0.231511i
\(342\) 28.0936 11.4315i 1.51913 0.618142i
\(343\) 16.6751 + 8.05859i 0.900371 + 0.435123i
\(344\) 3.21060 + 1.40100i 0.173104 + 0.0755370i
\(345\) −0.342710 + 0.0516552i −0.0184509 + 0.00278102i
\(346\) 1.95953 9.10626i 0.105345 0.489556i
\(347\) −20.3717 + 6.28384i −1.09361 + 0.337334i −0.788532 0.614994i \(-0.789159\pi\)
−0.305078 + 0.952327i \(0.598682\pi\)
\(348\) −0.967969 1.15367i −0.0518886 0.0618434i
\(349\) −15.2170 7.32813i −0.814548 0.392266i −0.0202508 0.999795i \(-0.506446\pi\)
−0.794297 + 0.607529i \(0.792161\pi\)
\(350\) 17.4122 + 5.14318i 0.930721 + 0.274915i
\(351\) 5.27874 + 10.9614i 0.281758 + 0.585077i
\(352\) 19.4941 + 21.5465i 1.03904 + 1.14843i
\(353\) 35.5599 2.66485i 1.89266 0.141836i 0.922768 0.385355i \(-0.125921\pi\)
0.969896 + 0.243520i \(0.0783021\pi\)
\(354\) 3.51842 0.0437945i 0.187002 0.00232765i
\(355\) −0.140831 + 0.456562i −0.00747452 + 0.0242318i
\(356\) 2.01204 16.0504i 0.106638 0.850672i
\(357\) 1.14033 1.97301i 0.0603524 0.104423i
\(358\) −11.0195 3.24944i −0.582401 0.171738i
\(359\) 0.318286 + 0.466840i 0.0167985 + 0.0246389i 0.834546 0.550938i \(-0.185730\pi\)
−0.817748 + 0.575577i \(0.804778\pi\)
\(360\) 2.89046 1.01122i 0.152341 0.0532960i
\(361\) 19.4655 + 33.7153i 1.02450 + 1.77449i
\(362\) −14.3117 1.97529i −0.752204 0.103819i
\(363\) −6.40227 + 1.46128i −0.336032 + 0.0766971i
\(364\) 12.4088 22.7593i 0.650397 1.19291i
\(365\) 3.23898 + 0.739276i 0.169536 + 0.0386955i
\(366\) −5.13827 1.94317i −0.268581 0.101571i
\(367\) −3.27051 0.492949i −0.170719 0.0257318i 0.0631264 0.998006i \(-0.479893\pi\)
−0.233845 + 0.972274i \(0.575131\pi\)
\(368\) −8.32369 1.46838i −0.433902 0.0765446i
\(369\) 0.652661 0.703401i 0.0339762 0.0366176i
\(370\) −0.578831 3.54069i −0.0300920 0.184072i
\(371\) −2.61496 1.02768i −0.135762 0.0533544i
\(372\) 2.58686 4.00489i 0.134123 0.207644i
\(373\) 3.08300 + 1.77997i 0.159632 + 0.0921635i 0.577688 0.816258i \(-0.303955\pi\)
−0.418056 + 0.908421i \(0.637288\pi\)
\(374\) 11.5720 + 8.99506i 0.598376 + 0.465124i
\(375\) −1.09914 1.18459i −0.0567595 0.0611721i
\(376\) 19.4681 3.68235i 1.00399 0.189903i
\(377\) −6.75595 5.38769i −0.347949 0.277480i
\(378\) 8.69010 + 3.29095i 0.446971 + 0.169268i
\(379\) 9.06638 + 11.3689i 0.465709 + 0.583980i 0.958114 0.286386i \(-0.0924538\pi\)
−0.492406 + 0.870366i \(0.663882\pi\)
\(380\) 2.66812 + 5.20487i 0.136872 + 0.267004i
\(381\) 0.0196230 0.0499986i 0.00100532 0.00256151i
\(382\) 11.6132 + 23.3665i 0.594183 + 1.19554i
\(383\) 8.92200 + 22.7329i 0.455893 + 1.16160i 0.955407 + 0.295291i \(0.0954166\pi\)
−0.499514 + 0.866306i \(0.666488\pi\)
\(384\) −4.82923 + 0.0595291i −0.246441 + 0.00303783i
\(385\) 4.70554 2.26341i 0.239816 0.115354i
\(386\) 1.09114 17.4767i 0.0555377 0.889540i
\(387\) −0.260791 + 3.48002i −0.0132568 + 0.176899i
\(388\) −3.18554 1.73492i −0.161721 0.0880771i
\(389\) −0.269271 + 0.394949i −0.0136526 + 0.0200247i −0.833004 0.553266i \(-0.813381\pi\)
0.819352 + 0.573291i \(0.194334\pi\)
\(390\) −0.976940 + 0.580367i −0.0494693 + 0.0293880i
\(391\) −4.26353 −0.215616
\(392\) −5.10566 19.1294i −0.257875 0.966178i
\(393\) −5.76732 −0.290923
\(394\) −11.1734 + 6.63775i −0.562908 + 0.334405i
\(395\) −3.18275 + 4.66824i −0.160142 + 0.234884i
\(396\) −13.8450 + 25.4213i −0.695738 + 1.27747i
\(397\) 1.91518 25.5563i 0.0961203 1.28264i −0.715567 0.698544i \(-0.753832\pi\)
0.811688 0.584092i \(-0.198549\pi\)
\(398\) −0.585218 + 9.37336i −0.0293343 + 0.469844i
\(399\) −1.91669 + 8.37987i −0.0959548 + 0.419518i
\(400\) −7.98145 17.6925i −0.399072 0.884625i
\(401\) −10.9978 28.0218i −0.549201 1.39934i −0.888593 0.458697i \(-0.848316\pi\)
0.339391 0.940645i \(-0.389779\pi\)
\(402\) 3.27554 + 6.59062i 0.163369 + 0.328710i
\(403\) 9.99462 25.4659i 0.497868 1.26855i
\(404\) −19.9731 + 10.2386i −0.993700 + 0.509390i
\(405\) 1.77112 + 2.22091i 0.0880077 + 0.110358i
\(406\) −6.57514 + 0.572080i −0.326319 + 0.0283918i
\(407\) 26.5150 + 21.1450i 1.31430 + 1.04812i
\(408\) −2.39374 + 0.452771i −0.118508 + 0.0224155i
\(409\) 21.3926 + 23.0558i 1.05780 + 1.14003i 0.989817 + 0.142347i \(0.0454649\pi\)
0.0679799 + 0.997687i \(0.478345\pi\)
\(410\) 0.146095 + 0.113561i 0.00721510 + 0.00560837i
\(411\) −4.81065 2.77743i −0.237292 0.137000i
\(412\) −17.8975 11.5604i −0.881745 0.569541i
\(413\) 8.69274 12.7374i 0.427742 0.626764i
\(414\) −1.35853 8.31007i −0.0667680 0.408417i
\(415\) 2.67998 2.88833i 0.131555 0.141783i
\(416\) −27.0926 + 5.82652i −1.32833 + 0.285668i
\(417\) −0.449965 0.0678213i −0.0220349 0.00332122i
\(418\) −51.7143 19.5571i −2.52943 0.956570i
\(419\) 15.4029 + 3.51561i 0.752480 + 0.171749i 0.581523 0.813530i \(-0.302457\pi\)
0.170957 + 0.985278i \(0.445314\pi\)
\(420\) −0.235481 + 0.835350i −0.0114903 + 0.0407609i
\(421\) −7.66198 + 1.74880i −0.373422 + 0.0852311i −0.405113 0.914267i \(-0.632768\pi\)
0.0316912 + 0.999498i \(0.489911\pi\)
\(422\) −8.26845 1.14121i −0.402502 0.0555532i
\(423\) 9.86934 + 17.0942i 0.479864 + 0.831148i
\(424\) 0.991869 + 2.83515i 0.0481694 + 0.137687i
\(425\) −5.51529 8.08944i −0.267531 0.392396i
\(426\) 0.720051 + 0.212328i 0.0348866 + 0.0102873i
\(427\) −19.8981 + 13.5530i −0.962939 + 0.655874i
\(428\) −14.4668 1.81352i −0.699280 0.0876597i
\(429\) 3.16612 10.2643i 0.152862 0.495566i
\(430\) −0.672916 + 0.00837593i −0.0324509 + 0.000403923i
\(431\) 19.4638 1.45861i 0.937537 0.0702587i 0.402810 0.915284i \(-0.368033\pi\)
0.534727 + 0.845025i \(0.320414\pi\)
\(432\) −3.39687 9.33515i −0.163432 0.449137i
\(433\) −12.6396 26.2463i −0.607418 1.26132i −0.947149 0.320794i \(-0.896050\pi\)
0.339731 0.940523i \(-0.389664\pi\)
\(434\) −7.86634 19.3575i −0.377596 0.929189i
\(435\) 0.260665 + 0.125530i 0.0124979 + 0.00601868i
\(436\) 3.26527 2.73966i 0.156378 0.131206i
\(437\) 15.3685 4.74054i 0.735173 0.226771i
\(438\) 1.09812 5.10316i 0.0524704 0.243839i
\(439\) −10.8913 + 1.64159i −0.519811 + 0.0783490i −0.403707 0.914888i \(-0.632279\pi\)
−0.116104 + 0.993237i \(0.537041\pi\)
\(440\) −5.11623 2.23255i −0.243907 0.106433i
\(441\) 16.3073 11.0962i 0.776536 0.528391i
\(442\) −12.9479 + 5.26857i −0.615868 + 0.250600i
\(443\) −19.9084 + 3.00071i −0.945879 + 0.142568i −0.603829 0.797114i \(-0.706359\pi\)
−0.342049 + 0.939682i \(0.611121\pi\)
\(444\) −5.55140 + 0.978631i −0.263458 + 0.0464438i
\(445\) 0.915994 + 2.96958i 0.0434223 + 0.140772i
\(446\) 34.8426 11.2243i 1.64985 0.531487i
\(447\) −8.74414 4.21096i −0.413584 0.199171i
\(448\) −11.9334 + 17.4813i −0.563798 + 0.825913i
\(449\) −6.57812 + 3.16786i −0.310441 + 0.149500i −0.582617 0.812747i \(-0.697971\pi\)
0.272176 + 0.962248i \(0.412257\pi\)
\(450\) 14.0098 13.3275i 0.660427 0.628263i
\(451\) −1.74427 + 0.130715i −0.0821342 + 0.00615511i
\(452\) −12.2672 29.1046i −0.577002 1.36896i
\(453\) −9.27858 2.86206i −0.435946 0.134471i
\(454\) 13.3418 + 7.48307i 0.626164 + 0.351198i
\(455\) −0.374435 + 4.96593i −0.0175538 + 0.232806i
\(456\) 8.12511 4.29362i 0.380493 0.201067i
\(457\) 1.46679 1.00004i 0.0686137 0.0467800i −0.528527 0.848916i \(-0.677256\pi\)
0.597141 + 0.802136i \(0.296303\pi\)
\(458\) −32.7926 15.2923i −1.53230 0.714560i
\(459\) −2.50549 4.33963i −0.116946 0.202556i
\(460\) 1.57359 0.400618i 0.0733690 0.0186789i
\(461\) 2.51018 + 10.9978i 0.116911 + 0.512218i 0.999143 + 0.0414035i \(0.0131829\pi\)
−0.882232 + 0.470815i \(0.843960\pi\)
\(462\) −3.64802 7.34852i −0.169721 0.341884i
\(463\) −6.42102 1.46555i −0.298410 0.0681101i 0.0706946 0.997498i \(-0.477478\pi\)
−0.369105 + 0.929388i \(0.620336\pi\)
\(464\) 5.05053 + 4.92694i 0.234465 + 0.228727i
\(465\) −0.136514 + 0.905711i −0.00633068 + 0.0420013i
\(466\) 9.58941 + 39.7280i 0.444221 + 1.84036i
\(467\) 25.9155 27.9302i 1.19922 1.29246i 0.253558 0.967320i \(-0.418399\pi\)
0.945667 0.325137i \(-0.105410\pi\)
\(468\) −14.3947 23.5580i −0.665394 1.08897i
\(469\) 31.8920 + 4.82190i 1.47263 + 0.222654i
\(470\) −3.11807 + 2.18320i −0.143826 + 0.100704i
\(471\) −5.30852 3.06487i −0.244604 0.141222i
\(472\) −16.3821 + 1.84482i −0.754046 + 0.0849146i
\(473\) 4.66329 4.32690i 0.214418 0.198951i
\(474\) 7.39643 + 4.90907i 0.339729 + 0.225481i
\(475\) 28.8750 + 23.0271i 1.32488 + 1.05656i
\(476\) −4.39605 + 9.72971i −0.201493 + 0.445961i
\(477\) −2.33950 + 1.86569i −0.107118 + 0.0854239i
\(478\) −17.1310 + 1.49842i −0.783553 + 0.0685362i
\(479\) 11.6457 29.6727i 0.532104 1.35578i −0.371907 0.928270i \(-0.621296\pi\)
0.904011 0.427509i \(-0.140609\pi\)
\(480\) 0.840940 0.392034i 0.0383835 0.0178938i
\(481\) −30.1090 + 11.8169i −1.37285 + 0.538805i
\(482\) −11.6202 + 12.8405i −0.529285 + 0.584868i
\(483\) 2.14971 + 1.03646i 0.0978151 + 0.0471605i
\(484\) 29.1653 9.79772i 1.32570 0.445351i
\(485\) 0.694913 + 0.0520765i 0.0315544 + 0.00236467i
\(486\) 11.6100 9.49747i 0.526641 0.430814i
\(487\) −18.6319 + 27.3280i −0.844292 + 1.23835i 0.124931 + 0.992165i \(0.460129\pi\)
−0.969223 + 0.246184i \(0.920823\pi\)
\(488\) 24.8602 + 6.66286i 1.12537 + 0.301614i
\(489\) 2.16078i 0.0977138i
\(490\) 2.40567 + 2.94628i 0.108677 + 0.133099i
\(491\) −13.4553 −0.607230 −0.303615 0.952795i \(-0.598194\pi\)
−0.303615 + 0.952795i \(0.598194\pi\)
\(492\) 0.175557 0.231748i 0.00791470 0.0104480i
\(493\) 2.94065 + 2.00490i 0.132440 + 0.0902963i
\(494\) 40.8143 33.3877i 1.83632 1.50218i
\(495\) 0.415581 5.54555i 0.0186790 0.249254i
\(496\) −10.1922 + 19.8767i −0.457642 + 0.892488i
\(497\) 2.57317 2.05011i 0.115423 0.0919599i
\(498\) −4.59021 4.15399i −0.205692 0.186145i
\(499\) 6.94117 + 17.6858i 0.310730 + 0.791726i 0.997872 + 0.0652033i \(0.0207696\pi\)
−0.687142 + 0.726523i \(0.741135\pi\)
\(500\) 5.67646 + 5.00992i 0.253859 + 0.224050i
\(501\) −8.66209 3.39962i −0.386994 0.151884i
\(502\) 35.1639 3.07573i 1.56944 0.137276i
\(503\) −11.9198 14.9470i −0.531479 0.666453i 0.441523 0.897250i \(-0.354438\pi\)
−0.973002 + 0.230796i \(0.925867\pi\)
\(504\) −20.3650 5.46810i −0.907127 0.243568i
\(505\) 2.68842 3.37117i 0.119633 0.150015i
\(506\) −8.48812 + 12.7889i −0.377343 + 0.568537i
\(507\) 3.19351 + 3.44178i 0.141829 + 0.152855i
\(508\) −0.0681658 + 0.242238i −0.00302437 + 0.0107476i
\(509\) −13.2403 + 22.9329i −0.586867 + 1.01648i 0.407773 + 0.913083i \(0.366306\pi\)
−0.994640 + 0.103400i \(0.967028\pi\)
\(510\) 0.383388 0.268440i 0.0169767 0.0118867i
\(511\) −15.5525 16.7771i −0.688004 0.742174i
\(512\) 22.4856 2.52941i 0.993732 0.111785i
\(513\) 13.8565 + 12.8569i 0.611779 + 0.567648i
\(514\) 25.4748 6.14902i 1.12365 0.271222i
\(515\) 4.04753 + 0.610067i 0.178356 + 0.0268828i
\(516\) 0.0263186 + 1.05704i 0.00115861 + 0.0465337i
\(517\) 8.00662 35.0793i 0.352131 1.54279i
\(518\) −10.4513 + 22.3849i −0.459203 + 0.983535i
\(519\) 2.74115 0.625649i 0.120323 0.0274629i
\(520\) 4.28376 3.16116i 0.187855 0.138626i
\(521\) −4.73371 + 2.73301i −0.207388 + 0.119735i −0.600097 0.799927i \(-0.704871\pi\)
0.392709 + 0.919663i \(0.371538\pi\)
\(522\) −2.97075 + 6.37047i −0.130026 + 0.278828i
\(523\) 12.6472 + 18.5501i 0.553025 + 0.811139i 0.996363 0.0852160i \(-0.0271580\pi\)
−0.443337 + 0.896355i \(0.646206\pi\)
\(524\) 26.8866 2.68933i 1.17455 0.117484i
\(525\) 0.814319 + 5.41952i 0.0355398 + 0.236527i
\(526\) 3.08345 + 1.72942i 0.134445 + 0.0754063i
\(527\) −3.32120 + 10.7670i −0.144674 + 0.469020i
\(528\) −3.40748 + 8.08168i −0.148291 + 0.351710i
\(529\) 1.38512 + 18.4832i 0.0602227 + 0.803616i
\(530\) −0.397721 0.418083i −0.0172759 0.0181603i
\(531\) −7.12590 14.7971i −0.309238 0.642139i
\(532\) 5.02786 39.9599i 0.217985 1.73248i
\(533\) 0.723819 1.50302i 0.0313521 0.0651032i
\(534\) 4.64754 1.49717i 0.201119 0.0647890i
\(535\) 2.67658 0.825617i 0.115719 0.0356945i
\(536\) −18.3435 29.1974i −0.792317 1.26113i
\(537\) −0.516856 3.42911i −0.0223040 0.147977i
\(538\) 0.796450 + 1.95733i 0.0343374 + 0.0843865i
\(539\) −35.5489 5.39148i −1.53120 0.232228i
\(540\) 1.33250 + 1.36625i 0.0573415 + 0.0587940i
\(541\) 4.95705 + 32.8879i 0.213120 + 1.41396i 0.797910 + 0.602777i \(0.205939\pi\)
−0.584790 + 0.811185i \(0.698823\pi\)
\(542\) 4.61364 21.4403i 0.198173 0.920941i
\(543\) −1.28540 4.16718i −0.0551620 0.178831i
\(544\) 10.9482 3.22698i 0.469402 0.138356i
\(545\) −0.355289 + 0.737765i −0.0152189 + 0.0316024i
\(546\) 7.80920 + 0.491156i 0.334203 + 0.0210195i
\(547\) 15.2783 7.35763i 0.653252 0.314589i −0.0777423 0.996973i \(-0.524771\pi\)
0.730994 + 0.682384i \(0.239057\pi\)
\(548\) 23.7219 + 10.7049i 1.01335 + 0.457289i
\(549\) 1.91613 + 25.5689i 0.0817782 + 1.09125i
\(550\) −35.2453 + 0.438706i −1.50287 + 0.0187065i
\(551\) −12.8292 3.95727i −0.546541 0.168585i
\(552\) −0.660177 2.46441i −0.0280990 0.104892i
\(553\) 36.2224 14.1971i 1.54033 0.603721i
\(554\) −4.10076 + 13.9066i −0.174225 + 0.590833i
\(555\) 0.894770 0.610044i 0.0379809 0.0258949i
\(556\) 2.12931 + 0.106355i 0.0903031 + 0.00451047i
\(557\) −20.8919 + 12.0619i −0.885216 + 0.511080i −0.872375 0.488838i \(-0.837421\pi\)
−0.0128415 + 0.999918i \(0.504088\pi\)
\(558\) −22.0443 3.04255i −0.933212 0.128801i
\(559\) 1.35007 + 5.91504i 0.0571019 + 0.250180i
\(560\) 0.708259 4.00412i 0.0299294 0.169205i
\(561\) −0.984470 + 4.31324i −0.0415643 + 0.182105i
\(562\) −0.137607 + 0.363869i −0.00580458 + 0.0153489i
\(563\) 1.77473 11.7746i 0.0747960 0.496239i −0.919797 0.392393i \(-0.871647\pi\)
0.994593 0.103845i \(-0.0331147\pi\)
\(564\) 3.49097 + 4.85605i 0.146996 + 0.204477i
\(565\) 4.44798 + 4.12712i 0.187128 + 0.173629i
\(566\) 2.39530 + 14.6520i 0.100682 + 0.615868i
\(567\) −1.45281 19.5065i −0.0610124 0.819194i
\(568\) −3.45581 0.654090i −0.145003 0.0274450i
\(569\) 20.5936 35.6691i 0.863328 1.49533i −0.00537005 0.999986i \(-0.501709\pi\)
0.868698 0.495342i \(-0.164957\pi\)
\(570\) −1.08350 + 1.39391i −0.0453828 + 0.0583843i
\(571\) 11.6000 10.7632i 0.485445 0.450427i −0.399083 0.916915i \(-0.630671\pi\)
0.884528 + 0.466488i \(0.154481\pi\)
\(572\) −9.97384 + 49.3275i −0.417027 + 2.06249i
\(573\) −4.91077 + 6.15791i −0.205150 + 0.257250i
\(574\) −0.390136 1.21297i −0.0162840 0.0506284i
\(575\) 8.01637 6.39284i 0.334306 0.266600i
\(576\) 9.77824 + 20.3110i 0.407427 + 0.846291i
\(577\) −18.6331 7.31295i −0.775705 0.304442i −0.0557340 0.998446i \(-0.517750\pi\)
−0.719971 + 0.694004i \(0.755845\pi\)
\(578\) −16.3734 + 8.13761i −0.681045 + 0.338480i
\(579\) 4.92023 1.93105i 0.204478 0.0802517i
\(580\) −1.27373 0.463657i −0.0528886 0.0192523i
\(581\) −26.4540 + 6.02519i −1.09750 + 0.249967i
\(582\) 0.0682271 1.09278i 0.00282810 0.0452974i
\(583\) 5.43943 + 0.407629i 0.225278 + 0.0168823i
\(584\) −2.73971 + 24.3025i −0.113370 + 1.00564i
\(585\) 4.38222 + 2.98775i 0.181182 + 0.123528i
\(586\) −12.4282 20.9205i −0.513404 0.864219i
\(587\) 12.9851i 0.535954i 0.963425 + 0.267977i \(0.0863551\pi\)
−0.963425 + 0.267977i \(0.913645\pi\)
\(588\) 4.58180 3.83712i 0.188950 0.158240i
\(589\) 42.5040i 1.75135i
\(590\) 2.72288 1.61757i 0.112099 0.0665944i
\(591\) −3.24129 2.20987i −0.133329 0.0909020i
\(592\) 25.4237 7.15091i 1.04491 0.293901i
\(593\) −1.05587 0.0791264i −0.0433593 0.00324933i 0.0530328 0.998593i \(-0.483111\pi\)
−0.0963921 + 0.995343i \(0.530730\pi\)
\(594\) −18.0053 1.12414i −0.738764 0.0461242i
\(595\) 0.000940551 2.05114i 3.85588e−5 0.0840887i
\(596\) 42.7279 + 15.5536i 1.75020 + 0.637101i
\(597\) −2.63889 + 1.03569i −0.108003 + 0.0423879i
\(598\) −6.51541 13.1095i −0.266435 0.536086i
\(599\) 21.6363 + 8.49161i 0.884034 + 0.346958i 0.763543 0.645757i \(-0.223458\pi\)
0.120491 + 0.992714i \(0.461553\pi\)
\(600\) 3.82185 4.44053i 0.156027 0.181284i
\(601\) −4.66643 + 3.72135i −0.190348 + 0.151797i −0.714027 0.700118i \(-0.753131\pi\)
0.523679 + 0.851916i \(0.324559\pi\)
\(602\) 3.85980 + 2.56433i 0.157314 + 0.104514i
\(603\) 21.4178 26.8571i 0.872202 1.09371i
\(604\) 44.5903 + 9.01599i 1.81436 + 0.366856i
\(605\) −4.33290 + 4.02034i −0.176157 + 0.163450i
\(606\) −5.34896 4.15780i −0.217287 0.168899i
\(607\) −4.97304 + 8.61355i −0.201849 + 0.349613i −0.949124 0.314902i \(-0.898028\pi\)
0.747275 + 0.664515i \(0.231362\pi\)
\(608\) −35.8763 + 23.8052i −1.45498 + 0.965427i
\(609\) −0.995310 1.72576i −0.0403320 0.0699311i
\(610\) −4.87976 + 0.797741i −0.197576 + 0.0322996i
\(611\) 25.1560 + 23.3413i 1.01770 + 0.944289i
\(612\) 6.63733 + 9.23274i 0.268298 + 0.373211i
\(613\) −0.909794 + 6.03609i −0.0367462 + 0.243795i −0.999662 0.0260078i \(-0.991721\pi\)
0.962916 + 0.269803i \(0.0869586\pi\)
\(614\) −6.14238 2.32290i −0.247886 0.0937447i
\(615\) −0.0124287 + 0.0544538i −0.000501175 + 0.00219579i
\(616\) 20.4333 + 32.5570i 0.823283 + 1.31176i
\(617\) 2.29313 + 10.0469i 0.0923181 + 0.404472i 0.999881 0.0154447i \(-0.00491640\pi\)
−0.907563 + 0.419917i \(0.862059\pi\)
\(618\) 0.879314 6.37094i 0.0353712 0.256277i
\(619\) −35.0425 + 20.2318i −1.40848 + 0.813184i −0.995241 0.0974405i \(-0.968934\pi\)
−0.413235 + 0.910625i \(0.635601\pi\)
\(620\) 0.214077 4.28599i 0.00859754 0.172129i
\(621\) 4.33590 2.95616i 0.173993 0.118627i
\(622\) 28.8210 + 8.49873i 1.15562 + 0.340768i
\(623\) 6.31682 20.4453i 0.253078 0.819125i
\(624\) −5.05022 6.66833i −0.202171 0.266947i
\(625\) 21.7941 + 6.72258i 0.871763 + 0.268903i
\(626\) 0.352860 + 28.3485i 0.0141031 + 1.13304i
\(627\) −1.24716 16.6422i −0.0498069 0.664627i
\(628\) 26.1769 + 11.8127i 1.04457 + 0.471380i
\(629\) 12.0028 5.78022i 0.478581 0.230473i
\(630\) 3.99819 0.651741i 0.159292 0.0259660i
\(631\) 14.6687 30.4599i 0.583952 1.21259i −0.374471 0.927239i \(-0.622176\pi\)
0.958423 0.285350i \(-0.0921100\pi\)
\(632\) −36.7705 19.4366i −1.46265 0.773146i
\(633\) −0.742633 2.40756i −0.0295170 0.0956918i
\(634\) 17.3319 + 3.72956i 0.688338 + 0.148120i
\(635\) −0.00720541 0.0478048i −0.000285938 0.00189707i
\(636\) −0.649065 + 0.633029i −0.0257371 + 0.0251012i
\(637\) 21.4053 26.7909i 0.848107 1.06149i
\(638\) 11.8684 4.82931i 0.469873 0.191194i
\(639\) −0.522232 3.46478i −0.0206592 0.137065i
\(640\) −3.73757 + 2.21975i −0.147740 + 0.0877435i
\(641\) −18.2384 + 5.62581i −0.720375 + 0.222206i −0.633202 0.773987i \(-0.718260\pi\)
−0.0871734 + 0.996193i \(0.527783\pi\)
\(642\) −1.34945 4.18899i −0.0532587 0.165326i
\(643\) −5.94328 + 12.3414i −0.234380 + 0.486696i −0.984673 0.174410i \(-0.944198\pi\)
0.750293 + 0.661106i \(0.229912\pi\)
\(644\) −10.5050 3.82945i −0.413955 0.150901i
\(645\) −0.0881370 0.183018i −0.00347039 0.00720634i
\(646\) −15.7357 + 14.9693i −0.619113 + 0.588961i
\(647\) 0.773420 + 10.3206i 0.0304063 + 0.405744i 0.991553 + 0.129704i \(0.0414029\pi\)
−0.961146 + 0.276039i \(0.910978\pi\)
\(648\) −14.7872 + 14.7854i −0.580897 + 0.580827i
\(649\) −8.82446 + 28.6082i −0.346390 + 1.12297i
\(650\) 16.4450 29.3204i 0.645026 1.15004i
\(651\) 4.29203 4.62145i 0.168218 0.181129i
\(652\) 1.00758 + 10.0733i 0.0394599 + 0.394502i
\(653\) 6.96511 + 10.2159i 0.272566 + 0.399781i 0.937978 0.346696i \(-0.112696\pi\)
−0.665412 + 0.746476i \(0.731744\pi\)
\(654\) 1.16604 + 0.543761i 0.0455957 + 0.0212627i
\(655\) −4.49559 + 2.59553i −0.175657 + 0.101416i
\(656\) −0.710362 + 1.16225i −0.0277350 + 0.0453781i
\(657\) −23.7534 + 5.42157i −0.926710 + 0.211515i
\(658\) 26.2087 0.314205i 1.02172 0.0122490i
\(659\) 7.88442 34.5439i 0.307133 1.34564i −0.551982 0.833856i \(-0.686128\pi\)
0.859115 0.511783i \(-0.171015\pi\)
\(660\) −0.0419397 1.68444i −0.00163250 0.0655668i
\(661\) −8.01586 1.20820i −0.311781 0.0469934i −0.00871201 0.999962i \(-0.502773\pi\)
−0.303069 + 0.952969i \(0.598011\pi\)
\(662\) −2.87165 11.8970i −0.111610 0.462389i
\(663\) −3.09310 2.86998i −0.120126 0.111461i
\(664\) 23.3361 + 17.2250i 0.905617 + 0.668460i
\(665\) 2.27724 + 7.39466i 0.0883074 + 0.286752i
\(666\) 15.0908 + 21.5528i 0.584756 + 0.835154i
\(667\) −1.86363 + 3.22790i −0.0721600 + 0.124985i
\(668\) 41.9670 + 11.8095i 1.62375 + 0.456923i
\(669\) 7.51556 + 8.09985i 0.290568 + 0.313158i
\(670\) 5.51932 + 3.66322i 0.213230 + 0.141522i
\(671\) 29.1419 36.5428i 1.12501 1.41072i
\(672\) −6.30466 1.03443i −0.243207 0.0399040i
\(673\) 4.52560 + 5.67492i 0.174449 + 0.218752i 0.861367 0.507982i \(-0.169609\pi\)
−0.686919 + 0.726734i \(0.741037\pi\)
\(674\) −1.12250 12.8332i −0.0432372 0.494317i
\(675\) 11.2178 + 4.40266i 0.431773 + 0.169458i
\(676\) −16.4927 14.5561i −0.634335 0.559849i
\(677\) −13.6555 34.7936i −0.524823 1.33723i −0.910085 0.414421i \(-0.863984\pi\)
0.385262 0.922807i \(-0.374111\pi\)
\(678\) 6.39706 7.06885i 0.245678 0.271477i
\(679\) −3.75026 2.99355i −0.143922 0.114882i
\(680\) −1.66214 + 1.43021i −0.0637402 + 0.0548462i
\(681\) −0.345061 + 4.60451i −0.0132228 + 0.176445i
\(682\) 25.6849 + 31.3980i 0.983524 + 1.20229i
\(683\) −12.9715 8.84380i −0.496340 0.338399i 0.289139 0.957287i \(-0.406631\pi\)
−0.785479 + 0.618888i \(0.787583\pi\)
\(684\) −34.1908 25.9007i −1.30732 0.990337i
\(685\) −4.99983 −0.191034
\(686\) −2.24633 26.0951i −0.0857653 0.996315i
\(687\) 10.9218i 0.416694i
\(688\) −0.615597 4.91555i −0.0234694 0.187403i
\(689\) −2.93057 + 4.29836i −0.111646 + 0.163754i
\(690\) 0.310343 + 0.379373i 0.0118145 + 0.0144425i
\(691\) 12.3634 + 0.926512i 0.470328 + 0.0352462i 0.307786 0.951456i \(-0.400412\pi\)
0.162541 + 0.986702i \(0.448031\pi\)
\(692\) −12.4872 + 4.19492i −0.474692 + 0.159467i
\(693\) −23.8891 + 29.9279i −0.907473 + 1.13687i
\(694\) 22.3546 + 20.2301i 0.848568 + 0.767925i
\(695\) −0.381268 + 0.149636i −0.0144623 + 0.00567603i
\(696\) −0.703534 + 2.01020i −0.0266674 + 0.0761964i
\(697\) −0.251027 + 0.639605i −0.00950831 + 0.0242268i
\(698\) 2.08128 + 23.7947i 0.0787777 + 0.900642i
\(699\) −9.64490 + 7.69155i −0.364804 + 0.290921i
\(700\) −6.32341 24.8855i −0.239003 0.940584i
\(701\) 33.0047 + 26.3204i 1.24657 + 0.994106i 0.999686 + 0.0250611i \(0.00797803\pi\)
0.246884 + 0.969045i \(0.420593\pi\)
\(702\) 9.51462 14.3355i 0.359106 0.541060i
\(703\) −36.8385 + 34.1812i −1.38939 + 1.28917i
\(704\) 12.1168 39.2649i 0.456668 1.47985i
\(705\) −0.995031 0.574481i −0.0374750 0.0216362i
\(706\) −28.9248 41.3107i −1.08860 1.55475i
\(707\) −28.3762 + 8.73864i −1.06720 + 0.328650i
\(708\) −2.59459 4.24623i −0.0975105 0.159583i
\(709\) 20.1568 21.7239i 0.757006 0.815858i −0.230561 0.973058i \(-0.574056\pi\)
0.987567 + 0.157200i \(0.0502467\pi\)
\(710\) 0.656832 0.158544i 0.0246505 0.00595004i
\(711\) 6.17554 40.9720i 0.231601 1.53657i
\(712\) −20.9682 + 9.14683i −0.785817 + 0.342792i
\(713\) −11.5042 2.62576i −0.430836 0.0983355i
\(714\) −3.22254 + 0.0386337i −0.120600 + 0.00144583i
\(715\) −2.15139 9.42586i −0.0804575 0.352507i
\(716\) 4.00854 + 15.7452i 0.149806 + 0.588424i
\(717\) −2.59536 4.49530i −0.0969256 0.167880i
\(718\) 0.337710 0.724184i 0.0126032 0.0270263i
\(719\) −11.4162 + 7.78340i −0.425751 + 0.290272i −0.757178 0.653209i \(-0.773422\pi\)
0.331427 + 0.943481i \(0.392470\pi\)
\(720\) −3.31726 2.78396i −0.123627 0.103752i
\(721\) −20.6528 19.1806i −0.769150 0.714324i
\(722\) 26.9328 48.0195i 1.00234 1.78710i
\(723\) −4.99514 1.54080i −0.185771 0.0573028i
\(724\) 7.93559 + 18.8276i 0.294924 + 0.699721i
\(725\) −8.53526 + 0.639629i −0.316991 + 0.0237552i
\(726\) 6.40102 + 6.72872i 0.237564 + 0.249726i
\(727\) −34.8691 + 16.7921i −1.29322 + 0.622783i −0.948754 0.316015i \(-0.897655\pi\)
−0.344468 + 0.938798i \(0.611941\pi\)
\(728\) −36.6347 + 1.35174i −1.35777 + 0.0500990i
\(729\) −15.9037 7.65883i −0.589027 0.283661i
\(730\) −1.44065 4.47209i −0.0533210 0.165519i
\(731\) −0.736566 2.38789i −0.0272429 0.0883193i
\(732\) 1.34874 + 7.65090i 0.0498510 + 0.282785i
\(733\) 21.2949 3.20969i 0.786544 0.118552i 0.256525 0.966538i \(-0.417423\pi\)
0.530020 + 0.847985i \(0.322184\pi\)
\(734\) 1.76292 + 4.33250i 0.0650705 + 0.159915i
\(735\) −0.499104 + 1.03397i −0.0184097 + 0.0381387i
\(736\) 4.22684 + 11.1810i 0.155803 + 0.412136i
\(737\) −61.9197 + 9.33289i −2.28084 + 0.343781i
\(738\) −1.32664 0.285474i −0.0488344 0.0105084i
\(739\) 6.69743 2.06588i 0.246369 0.0759948i −0.169111 0.985597i \(-0.554090\pi\)
0.415480 + 0.909602i \(0.363614\pi\)
\(740\) −3.88686 + 3.26119i −0.142884 + 0.119884i
\(741\) 14.3405 + 6.90604i 0.526813 + 0.253700i
\(742\) 0.639269 + 3.92168i 0.0234683 + 0.143969i
\(743\) 6.11648 + 12.7010i 0.224392 + 0.465955i 0.982521 0.186149i \(-0.0596008\pi\)
−0.758129 + 0.652104i \(0.773887\pi\)
\(744\) −6.73783 0.252518i −0.247021 0.00925775i
\(745\) −8.71111 + 0.652808i −0.319150 + 0.0239170i
\(746\) −0.0626610 5.03413i −0.00229418 0.184313i
\(747\) −8.51710 + 27.6117i −0.311624 + 1.01026i
\(748\) 2.57821 20.5669i 0.0942687 0.752002i
\(749\) −18.4281 5.69357i −0.673348 0.208038i
\(750\) −0.646382 + 2.19202i −0.0236025 + 0.0800412i
\(751\) −6.04553 8.86717i −0.220605 0.323568i 0.699942 0.714199i \(-0.253209\pi\)
−0.920547 + 0.390632i \(0.872257\pi\)
\(752\) −18.5389 21.0105i −0.676045 0.766176i
\(753\) 5.32736 + 9.22727i 0.194140 + 0.336260i
\(754\) −1.67083 + 12.1057i −0.0608479 + 0.440864i
\(755\) −8.52064 + 1.94478i −0.310098 + 0.0707778i
\(756\) −2.27553 12.9429i −0.0827601 0.470728i
\(757\) 23.7414 + 5.41882i 0.862896 + 0.196950i 0.630993 0.775789i \(-0.282648\pi\)
0.231903 + 0.972739i \(0.425505\pi\)
\(758\) 7.27424 19.2350i 0.264212 0.698648i
\(759\) −4.58147 0.690545i −0.166297 0.0250652i
\(760\) 4.40117 7.00349i 0.159647 0.254043i
\(761\) 9.82421 10.5880i 0.356128 0.383814i −0.529422 0.848358i \(-0.677591\pi\)
0.885550 + 0.464544i \(0.153782\pi\)
\(762\) −0.0749644 + 0.0122551i −0.00271567 + 0.000443957i
\(763\) 4.88444 2.81705i 0.176829 0.101984i
\(764\) 20.0220 30.9974i 0.724372 1.12145i
\(765\) −1.89184 1.09225i −0.0683996 0.0394905i
\(766\) 21.1954 27.2677i 0.765823 0.985221i
\(767\) −19.4211 20.9310i −0.701255 0.755773i
\(768\) 3.56051 + 5.82862i 0.128479 + 0.210322i
\(769\) 11.2064 + 8.93681i 0.404113 + 0.322270i 0.804365 0.594136i \(-0.202506\pi\)
−0.400251 + 0.916405i \(0.631077\pi\)
\(770\) −6.15075 4.08637i −0.221658 0.147263i
\(771\) 4.93206 + 6.18460i 0.177624 + 0.222733i
\(772\) −22.0372 + 11.2967i −0.793135 + 0.406576i
\(773\) −9.27271 + 23.6265i −0.333516 + 0.849786i 0.661488 + 0.749956i \(0.269925\pi\)
−0.995004 + 0.0998301i \(0.968170\pi\)
\(774\) 4.41954 2.19652i 0.158857 0.0789522i
\(775\) −9.89979 25.2243i −0.355611 0.906082i
\(776\) 0.191502 + 5.12626i 0.00687453 + 0.184022i
\(777\) −7.45704 0.00341942i −0.267520 0.000122671i
\(778\) 0.674692 + 0.0421238i 0.0241889 + 0.00151021i
\(779\) 0.193693 2.58465i 0.00693976 0.0926047i
\(780\) 1.41128 + 0.768615i 0.0505319 + 0.0275208i
\(781\) −3.59807 + 5.27740i −0.128749 + 0.188840i
\(782\) 3.07953 + 5.18382i 0.110124 + 0.185373i
\(783\) −4.38068 −0.156553
\(784\) −19.5706 + 20.0248i −0.698950 + 0.715170i
\(785\) −5.51728 −0.196920
\(786\) 4.16571 + 7.01219i 0.148586 + 0.250117i
\(787\) −7.08790 + 10.3960i −0.252656 + 0.370579i −0.931523 0.363683i \(-0.881519\pi\)
0.678866 + 0.734262i \(0.262472\pi\)
\(788\) 16.1410 + 8.79077i 0.575000 + 0.313158i
\(789\) −0.0797473 + 1.06415i −0.00283908 + 0.0378849i
\(790\) 7.97476 + 0.497897i 0.283729 + 0.0177144i
\(791\) −9.27868 40.7387i −0.329912 1.44850i
\(792\) 40.9086 1.52823i 1.45362 0.0543032i
\(793\) 16.2860 + 41.4961i 0.578333 + 1.47357i
\(794\) −32.4560 + 16.1307i −1.15182 + 0.572455i
\(795\) 0.0636349 0.162139i 0.00225690 0.00575048i
\(796\) 11.8193 6.05880i 0.418924 0.214748i
\(797\) −27.6207 34.6353i −0.978376 1.22684i −0.973929 0.226855i \(-0.927156\pi\)
−0.00444757 0.999990i \(-0.501416\pi\)
\(798\) 11.5731 3.72233i 0.409683 0.131769i
\(799\) −11.0506 8.81253i −0.390941 0.311765i
\(800\) −15.7464 + 22.4834i −0.556721 + 0.794910i
\(801\) −15.5013 16.7064i −0.547712 0.590293i
\(802\) −26.1267 + 33.6116i −0.922565 + 1.18687i
\(803\) 38.4632 + 22.2067i 1.35734 + 0.783658i
\(804\) 5.64729 8.74294i 0.199164 0.308340i
\(805\) 2.14213 0.159543i 0.0755003 0.00562315i
\(806\) −38.1817 + 6.24194i −1.34489 + 0.219863i
\(807\) −0.433854 + 0.467584i −0.0152724 + 0.0164597i
\(808\) 26.8751 + 16.8890i 0.945462 + 0.594153i
\(809\) −1.89997 0.286375i −0.0667995 0.0100684i 0.115557 0.993301i \(-0.463135\pi\)
−0.182357 + 0.983232i \(0.558373\pi\)
\(810\) 1.42102 3.75757i 0.0499297 0.132028i
\(811\) −52.3016 11.9375i −1.83656 0.419182i −0.843532 0.537079i \(-0.819528\pi\)
−0.993026 + 0.117897i \(0.962385\pi\)
\(812\) 5.44476 + 7.58117i 0.191074 + 0.266047i
\(813\) 6.45392 1.47307i 0.226349 0.0516627i
\(814\) 6.55747 47.5112i 0.229839 1.66527i
\(815\) −0.972440 1.68432i −0.0340631 0.0589990i
\(816\) 2.27949 + 2.58339i 0.0797980 + 0.0904368i
\(817\) 5.31009 + 7.78847i 0.185777 + 0.272484i
\(818\) 12.5805 42.6633i 0.439868 1.49169i
\(819\) −13.3272 34.0031i −0.465691 1.18816i
\(820\) 0.0325494 0.259654i 0.00113667 0.00906750i
\(821\) 7.03567 22.8091i 0.245547 0.796042i −0.745961 0.665990i \(-0.768009\pi\)
0.991507 0.130052i \(-0.0415145\pi\)
\(822\) 0.0977747 + 7.85515i 0.00341028 + 0.273980i
\(823\) −29.6909 + 2.22502i −1.03496 + 0.0775595i −0.581360 0.813646i \(-0.697479\pi\)
−0.453599 + 0.891206i \(0.649860\pi\)
\(824\) −1.12848 + 30.1107i −0.0393123 + 1.04895i
\(825\) −4.61636 9.58597i −0.160721 0.333740i
\(826\) −21.7654 1.36893i −0.757316 0.0476310i
\(827\) −0.589567 0.283920i −0.0205012 0.00987288i 0.423605 0.905847i \(-0.360764\pi\)
−0.444106 + 0.895974i \(0.646479\pi\)
\(828\) −9.12253 + 7.65409i −0.317030 + 0.265998i
\(829\) 0.488897 0.150805i 0.0169801 0.00523767i −0.286253 0.958154i \(-0.592410\pi\)
0.303234 + 0.952916i \(0.401934\pi\)
\(830\) −5.44751 1.17222i −0.189086 0.0406884i
\(831\) −4.32751 + 0.652267i −0.150120 + 0.0226269i
\(832\) 26.6531 + 28.7321i 0.924028 + 0.996106i
\(833\) −7.96702 + 11.6625i −0.276041 + 0.404081i
\(834\) 0.242547 + 0.596077i 0.00839872 + 0.0206404i
\(835\) −8.28202 + 1.24831i −0.286611 + 0.0431997i
\(836\) 13.5745 + 77.0028i 0.469484 + 2.66320i
\(837\) −4.08788 13.2526i −0.141298 0.458076i
\(838\) −6.85099 21.2669i −0.236663 0.734653i
\(839\) 14.6245 + 7.04280i 0.504895 + 0.243144i 0.668951 0.743307i \(-0.266744\pi\)
−0.164056 + 0.986451i \(0.552458\pi\)
\(840\) 1.18575 0.317061i 0.0409122 0.0109396i
\(841\) −23.3248 + 11.2326i −0.804304 + 0.387332i
\(842\) 7.66048 + 8.05266i 0.263998 + 0.277513i
\(843\) −0.117097 + 0.00877521i −0.00403304 + 0.000302234i
\(844\) 4.58473 + 10.8775i 0.157813 + 0.374418i
\(845\) 4.03826 + 1.24564i 0.138920 + 0.0428513i
\(846\) 13.6554 24.3467i 0.469482 0.837057i
\(847\) 40.2492 6.04771i 1.38298 0.207802i
\(848\) 2.73069 3.25378i 0.0937722 0.111735i
\(849\) −3.70271 + 2.52446i −0.127077 + 0.0866393i
\(850\) −5.85187 + 12.5487i −0.200718 + 0.430418i
\(851\) 6.97578 + 12.0824i 0.239127 + 0.414179i
\(852\) −0.261930 1.02884i −0.00897358 0.0352474i
\(853\) 8.81499 + 38.6210i 0.301820 + 1.32236i 0.867378 + 0.497650i \(0.165803\pi\)
−0.565559 + 0.824708i \(0.691339\pi\)
\(854\) 30.8507 + 14.4039i 1.05569 + 0.492891i
\(855\) 8.03383 + 1.83367i 0.274751 + 0.0627101i
\(856\) 8.24436 + 18.8994i 0.281786 + 0.645967i
\(857\) 8.51397 56.4865i 0.290832 1.92954i −0.0713862 0.997449i \(-0.522742\pi\)
0.362218 0.932093i \(-0.382020\pi\)
\(858\) −14.7667 + 3.56434i −0.504128 + 0.121685i
\(859\) 20.1514 21.7181i 0.687558 0.741011i −0.288748 0.957405i \(-0.593239\pi\)
0.976306 + 0.216394i \(0.0694296\pi\)
\(860\) 0.496228 + 0.812114i 0.0169212 + 0.0276929i
\(861\) 0.282057 0.261470i 0.00961247 0.00891087i
\(862\) −15.8321 22.6115i −0.539242 0.770150i
\(863\) 18.9718 + 10.9534i 0.645807 + 0.372857i 0.786848 0.617147i \(-0.211712\pi\)
−0.141041 + 0.990004i \(0.545045\pi\)
\(864\) −8.89659 + 10.8728i −0.302668 + 0.369901i
\(865\) 1.85514 1.72132i 0.0630767 0.0585266i
\(866\) −22.7820 + 34.3254i −0.774166 + 1.16642i
\(867\) −4.31498 3.44108i −0.146544 0.116865i
\(868\) −17.8540 + 23.5461i −0.606003 + 0.799207i
\(869\) −59.0526 + 47.0928i −2.00322 + 1.59752i
\(870\) −0.0356520 0.407599i −0.00120872 0.0138189i
\(871\) 21.8189 55.5936i 0.739305 1.88372i
\(872\) −5.68950 1.99123i −0.192671 0.0674314i
\(873\) −4.75724 + 1.86708i −0.161008 + 0.0631911i
\(874\) −16.8643 15.2616i −0.570445 0.516233i
\(875\) 6.24105 + 7.83339i 0.210986 + 0.264817i
\(876\) −6.99785 + 2.35084i −0.236435 + 0.0794275i
\(877\) 45.9316 + 3.44210i 1.55100 + 0.116231i 0.822480 0.568794i \(-0.192590\pi\)
0.728519 + 0.685025i \(0.240209\pi\)
\(878\) 9.86264 + 12.0564i 0.332848 + 0.406884i
\(879\) 4.13765 6.06882i 0.139560 0.204696i
\(880\) 0.980980 + 7.83313i 0.0330688 + 0.264055i
\(881\) 16.6463i 0.560828i 0.959879 + 0.280414i \(0.0904718\pi\)
−0.959879 + 0.280414i \(0.909528\pi\)
\(882\) −25.2700 11.8124i −0.850884 0.397745i
\(883\) −17.1768 −0.578047 −0.289023 0.957322i \(-0.593331\pi\)
−0.289023 + 0.957322i \(0.593331\pi\)
\(884\) 15.7580 + 11.9372i 0.529998 + 0.401492i
\(885\) 0.789878 + 0.538530i 0.0265514 + 0.0181025i
\(886\) 18.0282 + 22.0383i 0.605669 + 0.740390i
\(887\) 2.07469 27.6848i 0.0696613 0.929566i −0.847435 0.530900i \(-0.821854\pi\)
0.917096 0.398666i \(-0.130527\pi\)
\(888\) 5.19962 + 6.04280i 0.174488 + 0.202783i
\(889\) −0.144576 + 0.299864i −0.00484893 + 0.0100571i
\(890\) 2.94894 3.25862i 0.0988487 0.109229i
\(891\) 13.8738 + 35.3499i 0.464790 + 1.18426i
\(892\) −38.8138 34.2561i −1.29958 1.14698i
\(893\) 49.6316 + 19.4790i 1.66086 + 0.651839i
\(894\) 1.19597 + 13.6731i 0.0399991 + 0.457297i
\(895\) −1.94613 2.44037i −0.0650519 0.0815725i
\(896\) 29.8740 + 1.88252i 0.998020 + 0.0628906i
\(897\) 2.75512 3.45481i 0.0919907 0.115353i
\(898\) 8.60298 + 5.70988i 0.287085 + 0.190541i
\(899\) 6.69995 + 7.22083i 0.223456 + 0.240828i
\(900\) −26.3234 7.40739i −0.877446 0.246913i
\(901\) 1.07135 1.85564i 0.0356919 0.0618202i
\(902\) 1.41880 + 2.02635i 0.0472410 + 0.0674700i
\(903\) −0.209110 + 1.38305i −0.00695874 + 0.0460250i
\(904\) −26.5262 + 35.9372i −0.882248 + 1.19525i
\(905\) −2.87737 2.66981i −0.0956469 0.0887474i
\(906\) 3.22204 + 13.3486i 0.107045 + 0.443478i
\(907\) −39.9778 6.02569i −1.32744 0.200080i −0.553242 0.833020i \(-0.686610\pi\)
−0.774200 + 0.632941i \(0.781848\pi\)
\(908\) −0.538467 21.6267i −0.0178697 0.717706i
\(909\) −7.03649 + 30.8289i −0.233386 + 1.02253i
\(910\) 6.30827 3.13161i 0.209117 0.103812i
\(911\) −44.1054 + 10.0668i −1.46128 + 0.333527i −0.877967 0.478721i \(-0.841100\pi\)
−0.583312 + 0.812249i \(0.698243\pi\)
\(912\) −11.0891 6.77765i −0.367198 0.224430i
\(913\) 45.6164 26.3366i 1.50968 0.871616i
\(914\) −2.27536 1.06107i −0.0752622 0.0350972i
\(915\) −0.840759 1.23317i −0.0277946 0.0407672i
\(916\) 5.09289 + 50.9164i 0.168274 + 1.68233i
\(917\) 35.6440 + 2.68759i 1.17707 + 0.0887519i
\(918\) −3.46663 + 6.18079i −0.114416 + 0.203996i
\(919\) −8.94023 + 28.9835i −0.294911 + 0.956077i 0.679949 + 0.733259i \(0.262002\pi\)
−0.974860 + 0.222818i \(0.928474\pi\)
\(920\) −1.62369 1.62388i −0.0535314 0.0535379i
\(921\) −0.148132 1.97669i −0.00488112 0.0651340i
\(922\) 11.5586 10.9957i 0.380661 0.362123i
\(923\) −2.64311 5.48848i −0.0869991 0.180655i
\(924\) −6.29975 + 9.74325i −0.207246 + 0.320529i
\(925\) −13.9008 + 28.8653i −0.457055 + 0.949084i
\(926\) 2.85598 + 8.86555i 0.0938532 + 0.291340i
\(927\) −28.6847 + 8.84805i −0.942128 + 0.290608i
\(928\) 2.34244 9.69939i 0.0768944 0.318398i
\(929\) −5.34901 35.4884i −0.175495 1.16434i −0.887039 0.461694i \(-0.847242\pi\)
0.711544 0.702642i \(-0.247996\pi\)
\(930\) 1.19981 0.488211i 0.0393434 0.0160091i
\(931\) 15.7509 50.8973i 0.516214 1.66809i
\(932\) 41.3769 40.3546i 1.35535 1.32186i
\(933\) 1.35181 + 8.96866i 0.0442562 + 0.293621i
\(934\) −52.6776 11.3354i −1.72366 0.370906i
\(935\) 1.17375 + 3.80520i 0.0383857 + 0.124443i
\(936\) −18.2457 + 34.5176i −0.596380 + 1.12824i
\(937\) −9.84510 + 20.4436i −0.321625 + 0.667862i −0.997613 0.0690510i \(-0.978003\pi\)
0.675988 + 0.736913i \(0.263717\pi\)
\(938\) −17.1727 42.2586i −0.560709 1.37979i
\(939\) −7.71019 + 3.71303i −0.251612 + 0.121170i
\(940\) 4.90661 + 2.21418i 0.160036 + 0.0722188i
\(941\) 0.282896 + 3.77498i 0.00922214 + 0.123061i 0.999915 0.0130573i \(-0.00415637\pi\)
−0.990693 + 0.136118i \(0.956537\pi\)
\(942\) 0.107894 + 8.66810i 0.00351537 + 0.282422i
\(943\) −0.687601 0.212097i −0.0223914 0.00690682i
\(944\) 14.0757 + 18.5856i 0.458126 + 0.604911i
\(945\) 1.42122 + 2.08661i 0.0462324 + 0.0678774i
\(946\) −8.62913 2.54456i −0.280557 0.0827306i
\(947\) 20.9393 14.2762i 0.680437 0.463914i −0.173129 0.984899i \(-0.555388\pi\)
0.853566 + 0.520985i \(0.174435\pi\)
\(948\) 0.626287 12.5387i 0.0203408 0.407239i
\(949\) −36.6837 + 21.1793i −1.19080 + 0.687510i
\(950\) 7.14114 51.7401i 0.231689 1.67867i
\(951\) 1.19079 + 5.21721i 0.0386142 + 0.169180i
\(952\) 15.0051 1.68279i 0.486318 0.0545395i
\(953\) −2.07331 + 9.08377i −0.0671611 + 0.294252i −0.997343 0.0728464i \(-0.976792\pi\)
0.930182 + 0.367099i \(0.119649\pi\)
\(954\) 3.95820 + 1.49690i 0.128151 + 0.0484638i
\(955\) −1.05660 + 7.01010i −0.0341909 + 0.226842i
\(956\) 14.1955 + 19.7464i 0.459115 + 0.638644i
\(957\) 2.83521 + 2.63069i 0.0916494 + 0.0850382i
\(958\) −44.4891 + 7.27307i −1.43738 + 0.234982i
\(959\) 28.4371 + 19.4072i 0.918283 + 0.626692i
\(960\) −1.08406 0.739292i −0.0349879 0.0238605i
\(961\) −0.0925621 + 0.160322i −0.00298587 + 0.00517168i
\(962\) 36.1152 + 28.0727i 1.16440 + 0.905101i
\(963\) −15.0581 + 13.9719i −0.485240 + 0.450237i
\(964\) 24.0053 + 4.85378i 0.773159 + 0.156330i
\(965\) 2.96624 3.71955i 0.0954867 0.119737i
\(966\) −0.292546 3.36235i −0.00941251 0.108182i
\(967\) −9.36679 + 7.46976i −0.301216 + 0.240211i −0.762420 0.647082i \(-0.775989\pi\)
0.461204 + 0.887294i \(0.347417\pi\)
\(968\) −32.9785 28.3838i −1.05997 0.912289i
\(969\) −6.10255 2.39508i −0.196042 0.0769409i
\(970\) −0.438615 0.882524i −0.0140831 0.0283361i
\(971\) −9.76639 + 3.83303i −0.313418 + 0.123008i −0.516836 0.856084i \(-0.672890\pi\)
0.203418 + 0.979092i \(0.434795\pi\)
\(972\) −19.9333 7.25605i −0.639362 0.232738i
\(973\) 2.74933 + 0.628843i 0.0881395 + 0.0201598i
\(974\) 46.6844 + 2.91471i 1.49587 + 0.0933932i
\(975\) 10.1190 + 0.758314i 0.324067 + 0.0242855i
\(976\) −9.85535 35.0388i −0.315462 1.12156i
\(977\) 18.7130 + 12.7583i 0.598683 + 0.408175i 0.824392 0.566020i \(-0.191517\pi\)
−0.225709 + 0.974195i \(0.572470\pi\)
\(978\) −2.62718 + 1.56072i −0.0840080 + 0.0499064i
\(979\) 41.5441i 1.32775i
\(980\) 1.84463 5.05301i 0.0589244 0.161413i
\(981\) 6.00518i 0.191731i
\(982\) 9.71871 + 16.3596i 0.310137 + 0.522057i
\(983\) −21.7899 14.8561i −0.694991 0.473837i 0.163581 0.986530i \(-0.447696\pi\)
−0.858572 + 0.512693i \(0.828648\pi\)
\(984\) −0.408574 0.0460601i −0.0130249 0.00146834i
\(985\) −3.52110 0.263870i −0.112192 0.00840759i
\(986\) 0.313639 5.02352i 0.00998831 0.159981i
\(987\) 3.42947 + 7.12972i 0.109161 + 0.226942i
\(988\) −70.0744 25.5082i −2.22936 0.811523i
\(989\) 2.43609 0.956093i 0.0774630 0.0304020i
\(990\) −7.04272 + 3.50024i −0.223832 + 0.111245i
\(991\) 39.2983 + 15.4234i 1.24835 + 0.489942i 0.895217 0.445631i \(-0.147021\pi\)
0.353134 + 0.935573i \(0.385116\pi\)
\(992\) 31.5288 1.96466i 1.00104 0.0623781i
\(993\) 2.88826 2.30331i 0.0916563 0.0730935i
\(994\) −4.35121 1.64781i −0.138012 0.0522652i
\(995\) −1.59090 + 1.99492i −0.0504349 + 0.0632434i
\(996\) −1.73513 + 8.58141i −0.0549797 + 0.271912i
\(997\) 16.8353 15.6209i 0.533180 0.494719i −0.367009 0.930217i \(-0.619618\pi\)
0.900190 + 0.435498i \(0.143428\pi\)
\(998\) 16.4897 21.2138i 0.521973 0.671511i
\(999\) −8.19869 + 14.2005i −0.259395 + 0.449285i
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 392.2.bc.a.299.18 yes 648
8.3 odd 2 inner 392.2.bc.a.299.23 yes 648
49.10 odd 42 inner 392.2.bc.a.59.23 yes 648
392.59 even 42 inner 392.2.bc.a.59.18 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.2.bc.a.59.18 648 392.59 even 42 inner
392.2.bc.a.59.23 yes 648 49.10 odd 42 inner
392.2.bc.a.299.18 yes 648 1.1 even 1 trivial
392.2.bc.a.299.23 yes 648 8.3 odd 2 inner