Properties

Label 390.2.bd.c.37.1
Level $390$
Weight $2$
Character 390.37
Analytic conductor $3.114$
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] = [390,2,Mod(7,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bd (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.1
Character \(\chi\) \(=\) 390.37
Dual form 390.2.bd.c.253.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.10895 - 0.743195i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.0343211 - 0.0594459i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.10895 - 0.743195i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.0343211 - 0.0594459i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.19800 + 0.410849i) q^{10} +(-5.23449 - 1.40258i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.29893 - 3.36345i) q^{13} -0.0686422i q^{14} +(1.84473 + 1.26371i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.880498 - 3.28606i) q^{17} +1.00000 q^{18} +(0.295488 + 1.10278i) q^{19} +(-1.69810 + 1.45481i) q^{20} +(-0.0485374 + 0.0485374i) q^{21} +(-5.23449 + 1.40258i) q^{22} +(-0.462831 + 1.72731i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(3.89532 + 3.13472i) q^{25} +(-2.80663 - 2.26336i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.0343211 - 0.0594459i) q^{28} +(-3.37291 + 1.94735i) q^{29} +(2.22944 + 0.172035i) q^{30} +(-2.29267 - 2.29267i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.69312 + 2.70957i) q^{33} +(-2.40557 - 2.40557i) q^{34} +(-0.116561 + 0.0998611i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.20233 - 3.81454i) q^{37} +(0.807288 + 0.807288i) q^{38} +(0.384149 + 3.58503i) q^{39} +(-0.743195 + 2.10895i) q^{40} +(1.47354 - 5.49931i) q^{41} +(-0.0177659 + 0.0663033i) q^{42} +(8.55839 - 2.29321i) q^{43} +(-3.83191 + 3.83191i) q^{44} +(-1.45481 - 1.69810i) q^{45} +(0.462831 + 1.72731i) q^{46} +9.48215 q^{47} +(0.258819 + 0.965926i) q^{48} +(3.49764 + 6.05810i) q^{49} +(4.94081 + 0.767084i) q^{50} +3.40198i q^{51} +(-3.56230 - 0.556815i) q^{52} +(5.48446 - 5.48446i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(9.99688 + 6.84821i) q^{55} +(-0.0594459 - 0.0343211i) q^{56} -1.14168i q^{57} +(-1.94735 + 3.37291i) q^{58} +(-5.49573 + 1.47258i) q^{59} +(2.01677 - 0.965733i) q^{60} +(3.87879 - 6.71827i) q^{61} +(-3.13184 - 0.839174i) q^{62} +(0.0594459 - 0.0343211i) q^{63} -1.00000 q^{64} +(0.239686 + 8.05869i) q^{65} +5.41914 q^{66} +(0.899528 - 0.519343i) q^{67} +(-3.28606 - 0.880498i) q^{68} +(0.894121 - 1.54866i) q^{69} +(-0.0510145 + 0.144763i) q^{70} +(-5.00578 + 1.34130i) q^{71} +(0.500000 - 0.866025i) q^{72} -11.8364i q^{73} +(-3.81454 - 2.20233i) q^{74} +(-2.95127 - 4.03609i) q^{75} +(1.10278 + 0.295488i) q^{76} +(-0.263031 + 0.263031i) q^{77} +(2.12520 + 2.91265i) q^{78} +11.5811i q^{79} +(0.410849 + 2.19800i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.47354 - 5.49931i) q^{82} -4.93743 q^{83} +(0.0177659 + 0.0663033i) q^{84} +(-0.585260 + 7.58452i) q^{85} +(6.26518 - 6.26518i) q^{86} +(3.76199 - 1.00802i) q^{87} +(-1.40258 + 5.23449i) q^{88} +(-0.0552889 + 0.206341i) q^{89} +(-2.10895 - 0.743195i) q^{90} +(-0.244524 - 0.0382210i) q^{91} +(1.26448 + 1.26448i) q^{92} +(1.62116 + 2.80793i) q^{93} +(8.21179 - 4.74108i) q^{94} +(0.196408 - 2.54530i) q^{95} +(0.707107 + 0.707107i) q^{96} +(12.0237 + 6.94187i) q^{97} +(6.05810 + 3.49764i) q^{98} +(-3.83191 - 3.83191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 4 q^{11} + 20 q^{13} + 4 q^{15} - 16 q^{16} - 20 q^{17} + 32 q^{18} - 20 q^{19} + 8 q^{21} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{26} - 24 q^{29} + 4 q^{30} + 12 q^{31} - 12 q^{33} + 16 q^{34} + 12 q^{35} + 20 q^{37} + 4 q^{38} + 20 q^{39} - 28 q^{41} + 8 q^{42} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} + 28 q^{50} + 16 q^{52} - 4 q^{53} - 40 q^{55} - 12 q^{56} - 36 q^{59} - 4 q^{60} - 28 q^{61} - 36 q^{62} + 12 q^{63} - 32 q^{64} - 32 q^{65} - 36 q^{67} - 4 q^{68} + 20 q^{69} - 24 q^{70} - 4 q^{71} + 16 q^{72} - 24 q^{74} - 16 q^{76} - 20 q^{77} - 16 q^{78} + 16 q^{81} + 28 q^{82} - 40 q^{83} - 8 q^{84} + 88 q^{85} - 8 q^{86} - 16 q^{87} - 8 q^{88} + 16 q^{89} - 40 q^{91} + 20 q^{92} + 24 q^{94} - 8 q^{95} + 72 q^{97} + 72 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.10895 0.743195i −0.943150 0.332367i
\(6\) −0.965926 + 0.258819i −0.394338 + 0.105662i
\(7\) 0.0343211 0.0594459i 0.0129722 0.0224684i −0.859466 0.511192i \(-0.829204\pi\)
0.872439 + 0.488724i \(0.162537\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) −2.19800 + 0.410849i −0.695069 + 0.129922i
\(11\) −5.23449 1.40258i −1.57826 0.422893i −0.639872 0.768481i \(-0.721013\pi\)
−0.938386 + 0.345588i \(0.887679\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −1.29893 3.36345i −0.360259 0.932852i
\(14\) 0.0686422i 0.0183454i
\(15\) 1.84473 + 1.26371i 0.476308 + 0.326288i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.880498 3.28606i −0.213552 0.796987i −0.986671 0.162727i \(-0.947971\pi\)
0.773119 0.634261i \(-0.218695\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.295488 + 1.10278i 0.0677895 + 0.252994i 0.991502 0.130093i \(-0.0415276\pi\)
−0.923712 + 0.383087i \(0.874861\pi\)
\(20\) −1.69810 + 1.45481i −0.379707 + 0.325304i
\(21\) −0.0485374 + 0.0485374i −0.0105917 + 0.0105917i
\(22\) −5.23449 + 1.40258i −1.11600 + 0.299031i
\(23\) −0.462831 + 1.72731i −0.0965070 + 0.360169i −0.997244 0.0741966i \(-0.976361\pi\)
0.900737 + 0.434366i \(0.143027\pi\)
\(24\) −0.258819 + 0.965926i −0.0528312 + 0.197169i
\(25\) 3.89532 + 3.13472i 0.779065 + 0.626944i
\(26\) −2.80663 2.26336i −0.550426 0.443882i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −0.0343211 0.0594459i −0.00648608 0.0112342i
\(29\) −3.37291 + 1.94735i −0.626334 + 0.361614i −0.779331 0.626613i \(-0.784441\pi\)
0.152997 + 0.988227i \(0.451107\pi\)
\(30\) 2.22944 + 0.172035i 0.407038 + 0.0314092i
\(31\) −2.29267 2.29267i −0.411775 0.411775i 0.470582 0.882356i \(-0.344044\pi\)
−0.882356 + 0.470582i \(0.844044\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 4.69312 + 2.70957i 0.816967 + 0.471676i
\(34\) −2.40557 2.40557i −0.412551 0.412551i
\(35\) −0.116561 + 0.0998611i −0.0197025 + 0.0168796i
\(36\) 0.866025 0.500000i 0.144338 0.0833333i
\(37\) −2.20233 3.81454i −0.362060 0.627107i 0.626239 0.779631i \(-0.284593\pi\)
−0.988300 + 0.152524i \(0.951260\pi\)
\(38\) 0.807288 + 0.807288i 0.130959 + 0.130959i
\(39\) 0.384149 + 3.58503i 0.0615130 + 0.574064i
\(40\) −0.743195 + 2.10895i −0.117509 + 0.333454i
\(41\) 1.47354 5.49931i 0.230128 0.858848i −0.750157 0.661259i \(-0.770022\pi\)
0.980285 0.197589i \(-0.0633110\pi\)
\(42\) −0.0177659 + 0.0663033i −0.00274134 + 0.0102308i
\(43\) 8.55839 2.29321i 1.30514 0.349712i 0.461750 0.887010i \(-0.347222\pi\)
0.843392 + 0.537298i \(0.180555\pi\)
\(44\) −3.83191 + 3.83191i −0.577683 + 0.577683i
\(45\) −1.45481 1.69810i −0.216870 0.253138i
\(46\) 0.462831 + 1.72731i 0.0682408 + 0.254678i
\(47\) 9.48215 1.38311 0.691557 0.722322i \(-0.256925\pi\)
0.691557 + 0.722322i \(0.256925\pi\)
\(48\) 0.258819 + 0.965926i 0.0373573 + 0.139419i
\(49\) 3.49764 + 6.05810i 0.499663 + 0.865442i
\(50\) 4.94081 + 0.767084i 0.698736 + 0.108482i
\(51\) 3.40198i 0.476373i
\(52\) −3.56230 0.556815i −0.494002 0.0772163i
\(53\) 5.48446 5.48446i 0.753349 0.753349i −0.221754 0.975103i \(-0.571178\pi\)
0.975103 + 0.221754i \(0.0711782\pi\)
\(54\) −0.965926 0.258819i −0.131446 0.0352208i
\(55\) 9.99688 + 6.84821i 1.34798 + 0.923413i
\(56\) −0.0594459 0.0343211i −0.00794379 0.00458635i
\(57\) 1.14168i 0.151219i
\(58\) −1.94735 + 3.37291i −0.255700 + 0.442885i
\(59\) −5.49573 + 1.47258i −0.715482 + 0.191713i −0.598155 0.801380i \(-0.704099\pi\)
−0.117327 + 0.993093i \(0.537433\pi\)
\(60\) 2.01677 0.965733i 0.260364 0.124676i
\(61\) 3.87879 6.71827i 0.496629 0.860186i −0.503364 0.864075i \(-0.667904\pi\)
0.999992 + 0.00388852i \(0.00123776\pi\)
\(62\) −3.13184 0.839174i −0.397744 0.106575i
\(63\) 0.0594459 0.0343211i 0.00748948 0.00432405i
\(64\) −1.00000 −0.125000
\(65\) 0.239686 + 8.05869i 0.0297294 + 0.999558i
\(66\) 5.41914 0.667051
\(67\) 0.899528 0.519343i 0.109895 0.0634478i −0.444045 0.896004i \(-0.646457\pi\)
0.553940 + 0.832557i \(0.313124\pi\)
\(68\) −3.28606 0.880498i −0.398494 0.106776i
\(69\) 0.894121 1.54866i 0.107640 0.186437i
\(70\) −0.0510145 + 0.144763i −0.00609740 + 0.0173025i
\(71\) −5.00578 + 1.34130i −0.594077 + 0.159182i −0.543316 0.839528i \(-0.682831\pi\)
−0.0507612 + 0.998711i \(0.516165\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 11.8364i 1.38535i −0.721249 0.692676i \(-0.756432\pi\)
0.721249 0.692676i \(-0.243568\pi\)
\(74\) −3.81454 2.20233i −0.443431 0.256015i
\(75\) −2.95127 4.03609i −0.340783 0.466047i
\(76\) 1.10278 + 0.295488i 0.126497 + 0.0338948i
\(77\) −0.263031 + 0.263031i −0.0299752 + 0.0299752i
\(78\) 2.12520 + 2.91265i 0.240631 + 0.329793i
\(79\) 11.5811i 1.30298i 0.758657 + 0.651490i \(0.225856\pi\)
−0.758657 + 0.651490i \(0.774144\pi\)
\(80\) 0.410849 + 2.19800i 0.0459343 + 0.245744i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −1.47354 5.49931i −0.162725 0.607297i
\(83\) −4.93743 −0.541953 −0.270977 0.962586i \(-0.587347\pi\)
−0.270977 + 0.962586i \(0.587347\pi\)
\(84\) 0.0177659 + 0.0663033i 0.00193842 + 0.00723428i
\(85\) −0.585260 + 7.58452i −0.0634804 + 0.822656i
\(86\) 6.26518 6.26518i 0.675591 0.675591i
\(87\) 3.76199 1.00802i 0.403328 0.108071i
\(88\) −1.40258 + 5.23449i −0.149515 + 0.557999i
\(89\) −0.0552889 + 0.206341i −0.00586061 + 0.0218721i −0.968794 0.247866i \(-0.920271\pi\)
0.962934 + 0.269739i \(0.0869373\pi\)
\(90\) −2.10895 0.743195i −0.222303 0.0783396i
\(91\) −0.244524 0.0382210i −0.0256331 0.00400665i
\(92\) 1.26448 + 1.26448i 0.131831 + 0.131831i
\(93\) 1.62116 + 2.80793i 0.168106 + 0.291169i
\(94\) 8.21179 4.74108i 0.846981 0.489005i
\(95\) 0.196408 2.54530i 0.0201511 0.261142i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 12.0237 + 6.94187i 1.22082 + 0.704840i 0.965093 0.261909i \(-0.0843520\pi\)
0.255726 + 0.966749i \(0.417685\pi\)
\(98\) 6.05810 + 3.49764i 0.611960 + 0.353315i
\(99\) −3.83191 3.83191i −0.385122 0.385122i
\(100\) 4.66241 1.80609i 0.466241 0.180609i
\(101\) 4.74629 2.74027i 0.472273 0.272667i −0.244917 0.969544i \(-0.578761\pi\)
0.717191 + 0.696877i \(0.245428\pi\)
\(102\) 1.70099 + 2.94620i 0.168423 + 0.291718i
\(103\) −0.979342 0.979342i −0.0964974 0.0964974i 0.657210 0.753707i \(-0.271736\pi\)
−0.753707 + 0.657210i \(0.771736\pi\)
\(104\) −3.36345 + 1.29893i −0.329813 + 0.127371i
\(105\) 0.138436 0.0662901i 0.0135099 0.00646925i
\(106\) 2.00745 7.49191i 0.194981 0.727679i
\(107\) −2.80142 + 10.4550i −0.270824 + 1.01073i 0.687765 + 0.725933i \(0.258592\pi\)
−0.958589 + 0.284794i \(0.908075\pi\)
\(108\) −0.965926 + 0.258819i −0.0929463 + 0.0249049i
\(109\) −8.33989 + 8.33989i −0.798817 + 0.798817i −0.982909 0.184092i \(-0.941065\pi\)
0.184092 + 0.982909i \(0.441065\pi\)
\(110\) 12.0817 + 0.932283i 1.15194 + 0.0888897i
\(111\) 1.14001 + 4.25457i 0.108205 + 0.403826i
\(112\) −0.0686422 −0.00648608
\(113\) −5.18622 19.3553i −0.487879 1.82079i −0.566731 0.823903i \(-0.691792\pi\)
0.0788523 0.996886i \(-0.474874\pi\)
\(114\) −0.570838 0.988721i −0.0534639 0.0926022i
\(115\) 2.25981 3.29883i 0.210729 0.307618i
\(116\) 3.89470i 0.361614i
\(117\) 0.556815 3.56230i 0.0514775 0.329334i
\(118\) −4.02315 + 4.02315i −0.370361 + 0.370361i
\(119\) −0.225563 0.0604393i −0.0206773 0.00554046i
\(120\) 1.26371 1.84473i 0.115360 0.168400i
\(121\) 15.9064 + 9.18357i 1.44604 + 0.834870i
\(122\) 7.75759i 0.702339i
\(123\) −2.84665 + 4.93055i −0.256674 + 0.444572i
\(124\) −3.13184 + 0.839174i −0.281247 + 0.0753600i
\(125\) −5.88533 9.50594i −0.526400 0.850237i
\(126\) 0.0343211 0.0594459i 0.00305757 0.00529586i
\(127\) −10.2589 2.74887i −0.910331 0.243922i −0.226883 0.973922i \(-0.572854\pi\)
−0.683448 + 0.730000i \(0.739520\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −8.86030 −0.780106
\(130\) 4.23692 + 6.85919i 0.371603 + 0.601591i
\(131\) −19.3910 −1.69420 −0.847100 0.531433i \(-0.821654\pi\)
−0.847100 + 0.531433i \(0.821654\pi\)
\(132\) 4.69312 2.70957i 0.408483 0.235838i
\(133\) 0.0756969 + 0.0202829i 0.00656376 + 0.00175875i
\(134\) 0.519343 0.899528i 0.0448644 0.0777074i
\(135\) 0.965733 + 2.01677i 0.0831171 + 0.173576i
\(136\) −3.28606 + 0.880498i −0.281778 + 0.0755021i
\(137\) 6.01623 10.4204i 0.514001 0.890276i −0.485867 0.874033i \(-0.661496\pi\)
0.999868 0.0162432i \(-0.00517061\pi\)
\(138\) 1.78824i 0.152225i
\(139\) 3.76993 + 2.17657i 0.319761 + 0.184614i 0.651286 0.758832i \(-0.274230\pi\)
−0.331525 + 0.943447i \(0.607563\pi\)
\(140\) 0.0282016 + 0.150876i 0.00238347 + 0.0127513i
\(141\) −9.15906 2.45416i −0.771332 0.206678i
\(142\) −3.66449 + 3.66449i −0.307517 + 0.307517i
\(143\) 2.08176 + 19.4278i 0.174085 + 1.62463i
\(144\) 1.00000i 0.0833333i
\(145\) 8.56055 1.60013i 0.710915 0.132884i
\(146\) −5.91822 10.2507i −0.489796 0.848351i
\(147\) −1.81051 6.75693i −0.149329 0.557302i
\(148\) −4.40465 −0.362060
\(149\) −4.34708 16.2235i −0.356126 1.32908i −0.879061 0.476709i \(-0.841829\pi\)
0.522935 0.852373i \(-0.324837\pi\)
\(150\) −4.57392 2.01972i −0.373459 0.164910i
\(151\) 0.226120 0.226120i 0.0184014 0.0184014i −0.697846 0.716248i \(-0.745858\pi\)
0.716248 + 0.697846i \(0.245858\pi\)
\(152\) 1.10278 0.295488i 0.0894469 0.0239672i
\(153\) 0.880498 3.28606i 0.0711840 0.265662i
\(154\) −0.0962761 + 0.359307i −0.00775815 + 0.0289538i
\(155\) 3.13122 + 6.53901i 0.251505 + 0.525226i
\(156\) 3.29680 + 1.45983i 0.263955 + 0.116880i
\(157\) −16.0083 16.0083i −1.27760 1.27760i −0.942006 0.335597i \(-0.891062\pi\)
−0.335597 0.942006i \(-0.608938\pi\)
\(158\) 5.79057 + 10.0296i 0.460673 + 0.797910i
\(159\) −6.71707 + 3.87810i −0.532698 + 0.307553i
\(160\) 1.45481 + 1.69810i 0.115012 + 0.134247i
\(161\) 0.0867966 + 0.0867966i 0.00684053 + 0.00684053i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 9.90998 + 5.72153i 0.776209 + 0.448145i 0.835085 0.550121i \(-0.185418\pi\)
−0.0588758 + 0.998265i \(0.518752\pi\)
\(164\) −4.02577 4.02577i −0.314360 0.314360i
\(165\) −7.88380 9.20225i −0.613753 0.716394i
\(166\) −4.27594 + 2.46871i −0.331877 + 0.191609i
\(167\) −3.34397 5.79193i −0.258764 0.448193i 0.707147 0.707067i \(-0.249982\pi\)
−0.965911 + 0.258874i \(0.916649\pi\)
\(168\) 0.0485374 + 0.0485374i 0.00374474 + 0.00374474i
\(169\) −9.62555 + 8.73778i −0.740427 + 0.672137i
\(170\) 3.28541 + 6.86102i 0.251979 + 0.526216i
\(171\) −0.295488 + 1.10278i −0.0225965 + 0.0843313i
\(172\) 2.29321 8.55839i 0.174856 0.652571i
\(173\) 15.7568 4.22203i 1.19797 0.320995i 0.395938 0.918277i \(-0.370420\pi\)
0.802031 + 0.597282i \(0.203753\pi\)
\(174\) 2.75397 2.75397i 0.208778 0.208778i
\(175\) 0.320038 0.123974i 0.0241926 0.00937155i
\(176\) 1.40258 + 5.23449i 0.105723 + 0.394565i
\(177\) 5.68959 0.427656
\(178\) 0.0552889 + 0.206341i 0.00414408 + 0.0154659i
\(179\) 7.70365 + 13.3431i 0.575798 + 0.997312i 0.995954 + 0.0898598i \(0.0286419\pi\)
−0.420156 + 0.907452i \(0.638025\pi\)
\(180\) −2.19800 + 0.410849i −0.163829 + 0.0306228i
\(181\) 9.32410i 0.693055i −0.938040 0.346527i \(-0.887361\pi\)
0.938040 0.346527i \(-0.112639\pi\)
\(182\) −0.230874 + 0.0891616i −0.0171136 + 0.00660910i
\(183\) −5.48544 + 5.48544i −0.405496 + 0.405496i
\(184\) 1.72731 + 0.462831i 0.127339 + 0.0341204i
\(185\) 1.80965 + 9.68143i 0.133048 + 0.711793i
\(186\) 2.80793 + 1.62116i 0.205887 + 0.118869i
\(187\) 18.4358i 1.34816i
\(188\) 4.74108 8.21179i 0.345779 0.598906i
\(189\) −0.0663033 + 0.0177659i −0.00482285 + 0.00129228i
\(190\) −1.10256 2.30250i −0.0799878 0.167041i
\(191\) −12.1228 + 20.9972i −0.877172 + 1.51931i −0.0227417 + 0.999741i \(0.507240\pi\)
−0.854431 + 0.519566i \(0.826094\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) −21.6408 + 12.4943i −1.55774 + 0.899361i −0.560267 + 0.828312i \(0.689301\pi\)
−0.997473 + 0.0710490i \(0.977365\pi\)
\(194\) 13.8837 0.996795
\(195\) 1.85422 7.84614i 0.132784 0.561873i
\(196\) 6.99529 0.499663
\(197\) −6.09186 + 3.51714i −0.434027 + 0.250586i −0.701061 0.713101i \(-0.747290\pi\)
0.267034 + 0.963687i \(0.413957\pi\)
\(198\) −5.23449 1.40258i −0.371999 0.0996769i
\(199\) 11.0905 19.2092i 0.786182 1.36171i −0.142108 0.989851i \(-0.545388\pi\)
0.928290 0.371856i \(-0.121279\pi\)
\(200\) 3.13472 3.89532i 0.221658 0.275441i
\(201\) −1.00329 + 0.268832i −0.0707669 + 0.0189619i
\(202\) 2.74027 4.74629i 0.192805 0.333948i
\(203\) 0.267341i 0.0187637i
\(204\) 2.94620 + 1.70099i 0.206276 + 0.119093i
\(205\) −7.19467 + 10.5026i −0.502497 + 0.733536i
\(206\) −1.33781 0.358464i −0.0932094 0.0249754i
\(207\) −1.26448 + 1.26448i −0.0878873 + 0.0878873i
\(208\) −2.26336 + 2.80663i −0.156936 + 0.194605i
\(209\) 6.18691i 0.427958i
\(210\) 0.0867436 0.126627i 0.00598588 0.00873807i
\(211\) −10.1019 17.4970i −0.695443 1.20454i −0.970031 0.242981i \(-0.921875\pi\)
0.274588 0.961562i \(-0.411459\pi\)
\(212\) −2.00745 7.49191i −0.137872 0.514547i
\(213\) 5.18237 0.355090
\(214\) 2.80142 + 10.4550i 0.191501 + 0.714692i
\(215\) −19.7535 1.52428i −1.34718 0.103955i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) −0.214976 + 0.0576027i −0.0145935 + 0.00391033i
\(218\) −3.05261 + 11.3925i −0.206749 + 0.771598i
\(219\) −3.06350 + 11.4331i −0.207012 + 0.772579i
\(220\) 10.9292 5.23345i 0.736844 0.352839i
\(221\) −9.90879 + 7.22988i −0.666537 + 0.486335i
\(222\) 3.11456 + 3.11456i 0.209036 + 0.209036i
\(223\) −9.09923 15.7603i −0.609329 1.05539i −0.991351 0.131236i \(-0.958105\pi\)
0.382022 0.924153i \(-0.375228\pi\)
\(224\) −0.0594459 + 0.0343211i −0.00397190 + 0.00229318i
\(225\) 1.80609 + 4.66241i 0.120406 + 0.310827i
\(226\) −14.1690 14.1690i −0.942510 0.942510i
\(227\) 13.7492 + 7.93810i 0.912566 + 0.526870i 0.881256 0.472639i \(-0.156699\pi\)
0.0313104 + 0.999510i \(0.490032\pi\)
\(228\) −0.988721 0.570838i −0.0654797 0.0378047i
\(229\) −6.57629 6.57629i −0.434573 0.434573i 0.455608 0.890181i \(-0.349422\pi\)
−0.890181 + 0.455608i \(0.849422\pi\)
\(230\) 0.307640 3.98678i 0.0202852 0.262881i
\(231\) 0.322146 0.185991i 0.0211956 0.0122373i
\(232\) 1.94735 + 3.37291i 0.127850 + 0.221442i
\(233\) 16.6848 + 16.6848i 1.09306 + 1.09306i 0.995200 + 0.0978582i \(0.0311992\pi\)
0.0978582 + 0.995200i \(0.468801\pi\)
\(234\) −1.29893 3.36345i −0.0849139 0.219875i
\(235\) −19.9974 7.04709i −1.30448 0.459701i
\(236\) −1.47258 + 5.49573i −0.0958565 + 0.357741i
\(237\) 2.99742 11.1865i 0.194703 0.726643i
\(238\) −0.225563 + 0.0604393i −0.0146211 + 0.00391770i
\(239\) 13.8547 13.8547i 0.896186 0.896186i −0.0989101 0.995096i \(-0.531536\pi\)
0.995096 + 0.0989101i \(0.0315356\pi\)
\(240\) 0.172035 2.22944i 0.0111048 0.143910i
\(241\) −1.30150 4.85725i −0.0838368 0.312883i 0.911255 0.411843i \(-0.135115\pi\)
−0.995091 + 0.0989604i \(0.968448\pi\)
\(242\) 18.3671 1.18068
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) −3.87879 6.71827i −0.248314 0.430093i
\(245\) −2.87400 15.3756i −0.183613 0.982314i
\(246\) 5.69330i 0.362992i
\(247\) 3.32531 2.42629i 0.211584 0.154381i
\(248\) −2.29267 + 2.29267i −0.145584 + 0.145584i
\(249\) 4.76919 + 1.27790i 0.302235 + 0.0809837i
\(250\) −9.84981 5.28972i −0.622957 0.334551i
\(251\) 23.9886 + 13.8498i 1.51415 + 0.874192i 0.999863 + 0.0165711i \(0.00527499\pi\)
0.514282 + 0.857621i \(0.328058\pi\)
\(252\) 0.0686422i 0.00432405i
\(253\) 4.84537 8.39243i 0.304626 0.527628i
\(254\) −10.2589 + 2.74887i −0.643701 + 0.172479i
\(255\) 2.52834 7.17461i 0.158331 0.449291i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 14.6760 + 3.93242i 0.915463 + 0.245297i 0.685645 0.727936i \(-0.259520\pi\)
0.229818 + 0.973234i \(0.426187\pi\)
\(258\) −7.67324 + 4.43015i −0.477715 + 0.275809i
\(259\) −0.302345 −0.0187868
\(260\) 7.09888 + 3.82177i 0.440254 + 0.237016i
\(261\) −3.89470 −0.241076
\(262\) −16.7931 + 9.69551i −1.03748 + 0.598990i
\(263\) −10.0058 2.68104i −0.616982 0.165320i −0.0632266 0.997999i \(-0.520139\pi\)
−0.553755 + 0.832679i \(0.686806\pi\)
\(264\) 2.70957 4.69312i 0.166763 0.288841i
\(265\) −15.6425 + 7.49042i −0.960909 + 0.460133i
\(266\) 0.0756969 0.0202829i 0.00464128 0.00124363i
\(267\) 0.106810 0.185000i 0.00653666 0.0113218i
\(268\) 1.03869i 0.0634478i
\(269\) −3.23208 1.86604i −0.197063 0.113775i 0.398222 0.917289i \(-0.369628\pi\)
−0.595285 + 0.803515i \(0.702961\pi\)
\(270\) 1.84473 + 1.26371i 0.112267 + 0.0769067i
\(271\) −14.9084 3.99471i −0.905624 0.242661i −0.224194 0.974545i \(-0.571975\pi\)
−0.681430 + 0.731883i \(0.738642\pi\)
\(272\) −2.40557 + 2.40557i −0.145859 + 0.145859i
\(273\) 0.226300 + 0.100206i 0.0136963 + 0.00606475i
\(274\) 12.0325i 0.726907i
\(275\) −15.9934 21.8721i −0.964435 1.31894i
\(276\) −0.894121 1.54866i −0.0538198 0.0932186i
\(277\) 6.56759 + 24.5106i 0.394609 + 1.47270i 0.822446 + 0.568843i \(0.192609\pi\)
−0.427837 + 0.903856i \(0.640724\pi\)
\(278\) 4.35314 0.261084
\(279\) −0.839174 3.13184i −0.0502400 0.187498i
\(280\) 0.0998611 + 0.116561i 0.00596784 + 0.00696587i
\(281\) −8.33382 + 8.33382i −0.497154 + 0.497154i −0.910551 0.413397i \(-0.864342\pi\)
0.413397 + 0.910551i \(0.364342\pi\)
\(282\) −9.15906 + 2.45416i −0.545414 + 0.146143i
\(283\) 5.47731 20.4416i 0.325592 1.21513i −0.588123 0.808772i \(-0.700133\pi\)
0.913715 0.406355i \(-0.133201\pi\)
\(284\) −1.34130 + 5.00578i −0.0795912 + 0.297039i
\(285\) −0.848488 + 2.40774i −0.0502601 + 0.142622i
\(286\) 11.5167 + 15.7841i 0.681000 + 0.933332i
\(287\) −0.276338 0.276338i −0.0163117 0.0163117i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 4.69950 2.71326i 0.276441 0.159603i
\(290\) 6.61359 5.66603i 0.388363 0.332721i
\(291\) −9.81729 9.81729i −0.575500 0.575500i
\(292\) −10.2507 5.91822i −0.599875 0.346338i
\(293\) 9.27799 + 5.35665i 0.542026 + 0.312939i 0.745900 0.666058i \(-0.232020\pi\)
−0.203874 + 0.978997i \(0.565353\pi\)
\(294\) −4.94642 4.94642i −0.288481 0.288481i
\(295\) 12.6846 + 0.978809i 0.738526 + 0.0569885i
\(296\) −3.81454 + 2.20233i −0.221716 + 0.128008i
\(297\) 2.70957 + 4.69312i 0.157225 + 0.272322i
\(298\) −11.8764 11.8764i −0.687983 0.687983i
\(299\) 6.41090 0.686951i 0.370752 0.0397274i
\(300\) −4.97099 + 0.537829i −0.287000 + 0.0310516i
\(301\) 0.157411 0.587467i 0.00907303 0.0338610i
\(302\) 0.0827656 0.308886i 0.00476263 0.0177744i
\(303\) −5.29380 + 1.41847i −0.304121 + 0.0814889i
\(304\) 0.807288 0.807288i 0.0463011 0.0463011i
\(305\) −13.1732 + 11.2858i −0.754293 + 0.646222i
\(306\) −0.880498 3.28606i −0.0503347 0.187852i
\(307\) −18.5230 −1.05716 −0.528582 0.848882i \(-0.677276\pi\)
−0.528582 + 0.848882i \(0.677276\pi\)
\(308\) 0.0962761 + 0.359307i 0.00548584 + 0.0204734i
\(309\) 0.692499 + 1.19944i 0.0393949 + 0.0682340i
\(310\) 5.98122 + 4.09734i 0.339710 + 0.232713i
\(311\) 2.97373i 0.168625i 0.996439 + 0.0843124i \(0.0268694\pi\)
−0.996439 + 0.0843124i \(0.973131\pi\)
\(312\) 3.58503 0.384149i 0.202962 0.0217481i
\(313\) 9.69581 9.69581i 0.548040 0.548040i −0.377834 0.925873i \(-0.623331\pi\)
0.925873 + 0.377834i \(0.123331\pi\)
\(314\) −21.8678 5.85945i −1.23407 0.330668i
\(315\) −0.150876 + 0.0282016i −0.00850088 + 0.00158898i
\(316\) 10.0296 + 5.79057i 0.564207 + 0.325745i
\(317\) 6.45697i 0.362659i 0.983422 + 0.181330i \(0.0580401\pi\)
−0.983422 + 0.181330i \(0.941960\pi\)
\(318\) −3.87810 + 6.71707i −0.217473 + 0.376674i
\(319\) 20.3868 5.46262i 1.14144 0.305848i
\(320\) 2.10895 + 0.743195i 0.117894 + 0.0415458i
\(321\) 5.41193 9.37374i 0.302064 0.523191i
\(322\) 0.118566 + 0.0317698i 0.00660745 + 0.00177046i
\(323\) 3.36361 1.94198i 0.187156 0.108055i
\(324\) 1.00000 0.0555556
\(325\) 5.48369 17.1735i 0.304181 0.952614i
\(326\) 11.4431 0.633772
\(327\) 10.2142 5.89719i 0.564849 0.326116i
\(328\) −5.49931 1.47354i −0.303649 0.0813624i
\(329\) 0.325438 0.563675i 0.0179420 0.0310764i
\(330\) −11.4287 4.02748i −0.629129 0.221705i
\(331\) 19.5523 5.23904i 1.07469 0.287963i 0.322274 0.946647i \(-0.395553\pi\)
0.752420 + 0.658683i \(0.228886\pi\)
\(332\) −2.46871 + 4.27594i −0.135488 + 0.234673i
\(333\) 4.40465i 0.241374i
\(334\) −5.79193 3.34397i −0.316920 0.182974i
\(335\) −2.28303 + 0.426743i −0.124735 + 0.0233154i
\(336\) 0.0663033 + 0.0177659i 0.00361714 + 0.000969210i
\(337\) −14.2043 + 14.2043i −0.773758 + 0.773758i −0.978761 0.205004i \(-0.934279\pi\)
0.205004 + 0.978761i \(0.434279\pi\)
\(338\) −3.96708 + 12.3799i −0.215781 + 0.673379i
\(339\) 20.0380i 1.08832i
\(340\) 6.27576 + 4.29911i 0.340351 + 0.233152i
\(341\) 8.78530 + 15.2166i 0.475750 + 0.824024i
\(342\) 0.295488 + 1.10278i 0.0159781 + 0.0596313i
\(343\) 0.960668 0.0518712
\(344\) −2.29321 8.55839i −0.123642 0.461437i
\(345\) −3.03661 + 2.60155i −0.163486 + 0.140062i
\(346\) 11.5348 11.5348i 0.620114 0.620114i
\(347\) 27.0576 7.25007i 1.45253 0.389204i 0.555626 0.831432i \(-0.312479\pi\)
0.896903 + 0.442228i \(0.145812\pi\)
\(348\) 1.00802 3.76199i 0.0540357 0.201664i
\(349\) −5.33144 + 19.8972i −0.285385 + 1.06507i 0.663172 + 0.748467i \(0.269210\pi\)
−0.948557 + 0.316606i \(0.897457\pi\)
\(350\) 0.215174 0.267384i 0.0115015 0.0142923i
\(351\) −1.45983 + 3.29680i −0.0779201 + 0.175970i
\(352\) 3.83191 + 3.83191i 0.204242 + 0.204242i
\(353\) −2.81755 4.88014i −0.149963 0.259744i 0.781251 0.624218i \(-0.214582\pi\)
−0.931214 + 0.364474i \(0.881249\pi\)
\(354\) 4.92733 2.84480i 0.261885 0.151199i
\(355\) 11.5538 + 0.891549i 0.613211 + 0.0473185i
\(356\) 0.151052 + 0.151052i 0.00800574 + 0.00800574i
\(357\) 0.202234 + 0.116760i 0.0107034 + 0.00617959i
\(358\) 13.3431 + 7.70365i 0.705206 + 0.407151i
\(359\) 6.89818 + 6.89818i 0.364072 + 0.364072i 0.865310 0.501238i \(-0.167122\pi\)
−0.501238 + 0.865310i \(0.667122\pi\)
\(360\) −1.69810 + 1.45481i −0.0894977 + 0.0766750i
\(361\) 15.3257 8.84829i 0.806615 0.465699i
\(362\) −4.66205 8.07491i −0.245032 0.424408i
\(363\) −12.9875 12.9875i −0.681668 0.681668i
\(364\) −0.155362 + 0.192653i −0.00814320 + 0.0100978i
\(365\) −8.79678 + 24.9624i −0.460445 + 1.30659i
\(366\) −2.00781 + 7.49325i −0.104950 + 0.391679i
\(367\) −2.70714 + 10.1032i −0.141311 + 0.527382i 0.858580 + 0.512679i \(0.171347\pi\)
−0.999892 + 0.0147027i \(0.995320\pi\)
\(368\) 1.72731 0.462831i 0.0900423 0.0241267i
\(369\) 4.02577 4.02577i 0.209573 0.209573i
\(370\) 6.40791 + 7.47954i 0.333132 + 0.388843i
\(371\) −0.137796 0.514262i −0.00715401 0.0266991i
\(372\) 3.24232 0.168106
\(373\) −1.70438 6.36085i −0.0882497 0.329352i 0.907660 0.419706i \(-0.137867\pi\)
−0.995910 + 0.0903539i \(0.971200\pi\)
\(374\) 9.21792 + 15.9659i 0.476647 + 0.825577i
\(375\) 3.22447 + 10.7053i 0.166511 + 0.552818i
\(376\) 9.48215i 0.489005i
\(377\) 10.9310 + 8.81513i 0.562975 + 0.454002i
\(378\) −0.0485374 + 0.0485374i −0.00249649 + 0.00249649i
\(379\) 7.82771 + 2.09743i 0.402083 + 0.107738i 0.454192 0.890904i \(-0.349928\pi\)
−0.0521097 + 0.998641i \(0.516595\pi\)
\(380\) −2.10609 1.44275i −0.108040 0.0740113i
\(381\) 9.19789 + 5.31040i 0.471222 + 0.272060i
\(382\) 24.2455i 1.24051i
\(383\) 6.42723 11.1323i 0.328416 0.568833i −0.653782 0.756683i \(-0.726819\pi\)
0.982198 + 0.187850i \(0.0601519\pi\)
\(384\) 0.965926 0.258819i 0.0492922 0.0132078i
\(385\) 0.750202 0.359236i 0.0382338 0.0183083i
\(386\) −12.4943 + 21.6408i −0.635944 + 1.10149i
\(387\) 8.55839 + 2.29321i 0.435047 + 0.116571i
\(388\) 12.0237 6.94187i 0.610410 0.352420i
\(389\) 38.1804 1.93582 0.967912 0.251288i \(-0.0808540\pi\)
0.967912 + 0.251288i \(0.0808540\pi\)
\(390\) −2.31726 7.72207i −0.117339 0.391022i
\(391\) 6.08357 0.307659
\(392\) 6.05810 3.49764i 0.305980 0.176658i
\(393\) 18.7303 + 5.01876i 0.944818 + 0.253163i
\(394\) −3.51714 + 6.09186i −0.177191 + 0.306904i
\(395\) 8.60705 24.4240i 0.433068 1.22891i
\(396\) −5.23449 + 1.40258i −0.263043 + 0.0704822i
\(397\) 12.0611 20.8904i 0.605327 1.04846i −0.386673 0.922217i \(-0.626376\pi\)
0.992000 0.126240i \(-0.0402910\pi\)
\(398\) 22.1809i 1.11183i
\(399\) −0.0678680 0.0391836i −0.00339765 0.00196163i
\(400\) 0.767084 4.94081i 0.0383542 0.247040i
\(401\) 37.2272 + 9.97501i 1.85904 + 0.498128i 0.999907 0.0136248i \(-0.00433704\pi\)
0.859133 + 0.511753i \(0.171004\pi\)
\(402\) −0.734462 + 0.734462i −0.0366316 + 0.0366316i
\(403\) −4.73324 + 10.6893i −0.235779 + 0.532471i
\(404\) 5.48054i 0.272667i
\(405\) −0.410849 2.19800i −0.0204152 0.109219i
\(406\) 0.133670 + 0.231524i 0.00663395 + 0.0114903i
\(407\) 6.17787 + 23.0561i 0.306226 + 1.14285i
\(408\) 3.40198 0.168423
\(409\) 4.59831 + 17.1611i 0.227372 + 0.848564i 0.981440 + 0.191768i \(0.0614220\pi\)
−0.754068 + 0.656796i \(0.771911\pi\)
\(410\) −0.979448 + 12.6929i −0.0483715 + 0.626857i
\(411\) −8.50823 + 8.50823i −0.419680 + 0.419680i
\(412\) −1.33781 + 0.358464i −0.0659090 + 0.0176603i
\(413\) −0.101081 + 0.377239i −0.00497386 + 0.0185627i
\(414\) −0.462831 + 1.72731i −0.0227469 + 0.0848927i
\(415\) 10.4128 + 3.66947i 0.511143 + 0.180127i
\(416\) −0.556815 + 3.56230i −0.0273001 + 0.174656i
\(417\) −3.07814 3.07814i −0.150737 0.150737i
\(418\) −3.09346 5.35802i −0.151306 0.262070i
\(419\) −4.08722 + 2.35976i −0.199674 + 0.115282i −0.596503 0.802611i \(-0.703444\pi\)
0.396829 + 0.917892i \(0.370110\pi\)
\(420\) 0.0118089 0.153034i 0.000576214 0.00746728i
\(421\) −16.2123 16.2123i −0.790137 0.790137i 0.191379 0.981516i \(-0.438704\pi\)
−0.981516 + 0.191379i \(0.938704\pi\)
\(422\) −17.4970 10.1019i −0.851741 0.491753i
\(423\) 8.21179 + 4.74108i 0.399271 + 0.230519i
\(424\) −5.48446 5.48446i −0.266349 0.266349i
\(425\) 6.87106 15.5604i 0.333295 0.754790i
\(426\) 4.48806 2.59118i 0.217447 0.125543i
\(427\) −0.266249 0.461157i −0.0128847 0.0223169i
\(428\) 7.65363 + 7.65363i 0.369952 + 0.369952i
\(429\) 3.01746 19.3046i 0.145684 0.932035i
\(430\) −17.8692 + 8.55668i −0.861728 + 0.412640i
\(431\) 6.81996 25.4525i 0.328506 1.22600i −0.582234 0.813021i \(-0.697821\pi\)
0.910740 0.412980i \(-0.135512\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) −19.3655 + 5.18896i −0.930645 + 0.249366i −0.692130 0.721773i \(-0.743327\pi\)
−0.238515 + 0.971139i \(0.576661\pi\)
\(434\) −0.157374 + 0.157374i −0.00755418 + 0.00755418i
\(435\) −8.68300 0.670025i −0.416318 0.0321252i
\(436\) 3.05261 + 11.3925i 0.146194 + 0.545602i
\(437\) −2.04160 −0.0976628
\(438\) 3.06350 + 11.4331i 0.146380 + 0.546296i
\(439\) 3.87810 + 6.71707i 0.185092 + 0.320588i 0.943607 0.331067i \(-0.107408\pi\)
−0.758516 + 0.651655i \(0.774075\pi\)
\(440\) 6.84821 9.99688i 0.326476 0.476583i
\(441\) 6.99529i 0.333109i
\(442\) −4.96632 + 11.2157i −0.236224 + 0.533474i
\(443\) −7.27869 + 7.27869i −0.345821 + 0.345821i −0.858550 0.512729i \(-0.828634\pi\)
0.512729 + 0.858550i \(0.328634\pi\)
\(444\) 4.25457 + 1.14001i 0.201913 + 0.0541024i
\(445\) 0.269953 0.394072i 0.0127970 0.0186808i
\(446\) −15.7603 9.09923i −0.746273 0.430861i
\(447\) 16.7958i 0.794415i
\(448\) −0.0343211 + 0.0594459i −0.00162152 + 0.00280855i
\(449\) 1.50763 0.403969i 0.0711496 0.0190645i −0.223069 0.974803i \(-0.571607\pi\)
0.294218 + 0.955738i \(0.404941\pi\)
\(450\) 3.89532 + 3.13472i 0.183627 + 0.147772i
\(451\) −15.4264 + 26.7193i −0.726402 + 1.25816i
\(452\) −19.3553 5.18622i −0.910395 0.243939i
\(453\) −0.276939 + 0.159891i −0.0130117 + 0.00751233i
\(454\) 15.8762 0.745107
\(455\) 0.487283 + 0.262335i 0.0228442 + 0.0122985i
\(456\) −1.14168 −0.0534639
\(457\) −7.69003 + 4.43984i −0.359725 + 0.207687i −0.668960 0.743298i \(-0.733260\pi\)
0.309235 + 0.950986i \(0.399927\pi\)
\(458\) −8.98337 2.40709i −0.419766 0.112476i
\(459\) −1.70099 + 2.94620i −0.0793955 + 0.137517i
\(460\) −1.72697 3.60647i −0.0805202 0.168153i
\(461\) 9.36262 2.50871i 0.436061 0.116842i −0.0341090 0.999418i \(-0.510859\pi\)
0.470170 + 0.882576i \(0.344193\pi\)
\(462\) 0.185991 0.322146i 0.00865309 0.0149876i
\(463\) 0.374437i 0.0174015i −0.999962 0.00870077i \(-0.997230\pi\)
0.999962 0.00870077i \(-0.00276958\pi\)
\(464\) 3.37291 + 1.94735i 0.156583 + 0.0904035i
\(465\) −1.33210 7.12662i −0.0617747 0.330489i
\(466\) 22.7919 + 6.10707i 1.05581 + 0.282904i
\(467\) −28.2026 + 28.2026i −1.30506 + 1.30506i −0.380122 + 0.924936i \(0.624118\pi\)
−0.924936 + 0.380122i \(0.875882\pi\)
\(468\) −2.80663 2.26336i −0.129737 0.104624i
\(469\) 0.0712977i 0.00329222i
\(470\) −20.8418 + 3.89573i −0.961359 + 0.179697i
\(471\) 11.3196 + 19.6061i 0.521579 + 0.903401i
\(472\) 1.47258 + 5.49573i 0.0677808 + 0.252961i
\(473\) −48.0152 −2.20774
\(474\) −2.99742 11.1865i −0.137676 0.513814i
\(475\) −2.30587 + 5.22194i −0.105801 + 0.239599i
\(476\) −0.165123 + 0.165123i −0.00756842 + 0.00756842i
\(477\) 7.49191 2.00745i 0.343031 0.0919149i
\(478\) 5.07117 18.9259i 0.231950 0.865649i
\(479\) 8.58585 32.0428i 0.392297 1.46407i −0.434038 0.900895i \(-0.642912\pi\)
0.826335 0.563179i \(-0.190422\pi\)
\(480\) −0.965733 2.01677i −0.0440795 0.0920525i
\(481\) −9.96933 + 12.3622i −0.454562 + 0.563670i
\(482\) −3.55576 3.55576i −0.161960 0.161960i
\(483\) −0.0613745 0.106304i −0.00279264 0.00483699i
\(484\) 15.9064 9.18357i 0.723018 0.417435i
\(485\) −20.1981 23.5760i −0.917150 1.07053i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) −14.6119 8.43618i −0.662128 0.382280i 0.130959 0.991388i \(-0.458194\pi\)
−0.793087 + 0.609108i \(0.791528\pi\)
\(488\) −6.71827 3.87879i −0.304122 0.175585i
\(489\) −8.09146 8.09146i −0.365909 0.365909i
\(490\) −10.1768 11.8787i −0.459740 0.536625i
\(491\) 33.3926 19.2792i 1.50699 0.870060i 0.507020 0.861934i \(-0.330747\pi\)
0.999967 0.00812541i \(-0.00258643\pi\)
\(492\) 2.84665 + 4.93055i 0.128337 + 0.222286i
\(493\) 9.36896 + 9.36896i 0.421957 + 0.421957i
\(494\) 1.66666 3.76388i 0.0749864 0.169345i
\(495\) 5.23345 + 10.9292i 0.235226 + 0.491229i
\(496\) −0.839174 + 3.13184i −0.0376800 + 0.140624i
\(497\) −0.0920695 + 0.343608i −0.00412988 + 0.0154129i
\(498\) 4.76919 1.27790i 0.213713 0.0572641i
\(499\) 12.4800 12.4800i 0.558682 0.558682i −0.370250 0.928932i \(-0.620728\pi\)
0.928932 + 0.370250i \(0.120728\pi\)
\(500\) −11.1751 + 0.343874i −0.499763 + 0.0153785i
\(501\) 1.73097 + 6.46006i 0.0773339 + 0.288614i
\(502\) 27.6996 1.23629
\(503\) −2.99916 11.1930i −0.133726 0.499072i 0.866274 0.499569i \(-0.166508\pi\)
−1.00000 0.000497269i \(0.999842\pi\)
\(504\) −0.0343211 0.0594459i −0.00152878 0.00264793i
\(505\) −12.0462 + 2.25167i −0.536050 + 0.100198i
\(506\) 9.69075i 0.430806i
\(507\) 11.5591 5.94877i 0.513356 0.264194i
\(508\) −7.51004 + 7.51004i −0.333204 + 0.333204i
\(509\) −2.85834 0.765891i −0.126694 0.0339475i 0.194915 0.980820i \(-0.437557\pi\)
−0.321609 + 0.946873i \(0.604224\pi\)
\(510\) −1.39770 7.47756i −0.0618912 0.331112i
\(511\) −0.703628 0.406240i −0.0311267 0.0179710i
\(512\) 1.00000i 0.0441942i
\(513\) 0.570838 0.988721i 0.0252031 0.0436531i
\(514\) 14.6760 3.93242i 0.647330 0.173452i
\(515\) 1.33754 + 2.79322i 0.0589390 + 0.123084i
\(516\) −4.43015 + 7.67324i −0.195026 + 0.337796i
\(517\) −49.6343 13.2995i −2.18291 0.584910i
\(518\) −0.261839 + 0.151173i −0.0115045 + 0.00664214i
\(519\) −16.3127 −0.716046
\(520\) 8.05869 0.239686i 0.353397 0.0105109i
\(521\) 7.20237 0.315542 0.157771 0.987476i \(-0.449569\pi\)
0.157771 + 0.987476i \(0.449569\pi\)
\(522\) −3.37291 + 1.94735i −0.147628 + 0.0852332i
\(523\) 13.2297 + 3.54489i 0.578495 + 0.155007i 0.536190 0.844097i \(-0.319863\pi\)
0.0423053 + 0.999105i \(0.486530\pi\)
\(524\) −9.69551 + 16.7931i −0.423550 + 0.733610i
\(525\) −0.341220 + 0.0369178i −0.0148921 + 0.00161122i
\(526\) −10.0058 + 2.68104i −0.436272 + 0.116899i
\(527\) −5.51516 + 9.55253i −0.240244 + 0.416115i
\(528\) 5.41914i 0.235838i
\(529\) 17.1492 + 9.90109i 0.745617 + 0.430482i
\(530\) −9.80156 + 14.3081i −0.425753 + 0.621505i
\(531\) −5.49573 1.47258i −0.238494 0.0639043i
\(532\) 0.0554140 0.0554140i 0.00240250 0.00240250i
\(533\) −20.4107 + 2.18707i −0.884084 + 0.0947327i
\(534\) 0.213620i 0.00924423i
\(535\) 13.6782 19.9671i 0.591360 0.863255i
\(536\) −0.519343 0.899528i −0.0224322 0.0388537i
\(537\) −3.98770 14.8823i −0.172082 0.642219i
\(538\) −3.73208 −0.160902
\(539\) −9.81144 36.6168i −0.422608 1.57720i
\(540\) 2.22944 + 0.172035i 0.0959398 + 0.00740321i
\(541\) −6.11226 + 6.11226i −0.262787 + 0.262787i −0.826185 0.563399i \(-0.809494\pi\)
0.563399 + 0.826185i \(0.309494\pi\)
\(542\) −14.9084 + 3.99471i −0.640373 + 0.171587i
\(543\) −2.41325 + 9.00639i −0.103563 + 0.386501i
\(544\) −0.880498 + 3.28606i −0.0377510 + 0.140889i
\(545\) 23.7866 11.3902i 1.01890 0.487904i
\(546\) 0.246084 0.0263688i 0.0105314 0.00112848i
\(547\) −1.96357 1.96357i −0.0839560 0.0839560i 0.663882 0.747838i \(-0.268908\pi\)
−0.747838 + 0.663882i \(0.768908\pi\)
\(548\) −6.01623 10.4204i −0.257001 0.445138i
\(549\) 6.71827 3.87879i 0.286729 0.165543i
\(550\) −24.7867 10.9452i −1.05691 0.466703i
\(551\) −3.14414 3.14414i −0.133945 0.133945i
\(552\) −1.54866 0.894121i −0.0659155 0.0380563i
\(553\) 0.688452 + 0.397478i 0.0292759 + 0.0169025i
\(554\) 17.9430 + 17.9430i 0.762325 + 0.762325i
\(555\) 0.757755 9.81991i 0.0321649 0.416832i
\(556\) 3.76993 2.17657i 0.159881 0.0923072i
\(557\) −16.2450 28.1371i −0.688321 1.19221i −0.972381 0.233400i \(-0.925015\pi\)
0.284060 0.958807i \(-0.408319\pi\)
\(558\) −2.29267 2.29267i −0.0970563 0.0970563i
\(559\) −18.8299 25.8070i −0.796419 1.09152i
\(560\) 0.144763 + 0.0510145i 0.00611735 + 0.00215576i
\(561\) 4.77155 17.8077i 0.201455 0.751840i
\(562\) −3.05039 + 11.3842i −0.128673 + 0.480214i
\(563\) −30.6558 + 8.21419i −1.29199 + 0.346187i −0.838414 0.545033i \(-0.816517\pi\)
−0.453572 + 0.891220i \(0.649850\pi\)
\(564\) −6.70489 + 6.70489i −0.282327 + 0.282327i
\(565\) −3.44724 + 44.6736i −0.145027 + 1.87943i
\(566\) −5.47731 20.4416i −0.230229 0.859225i
\(567\) 0.0686422 0.00288270
\(568\) 1.34130 + 5.00578i 0.0562795 + 0.210038i
\(569\) 8.23444 + 14.2625i 0.345206 + 0.597914i 0.985391 0.170307i \(-0.0544759\pi\)
−0.640186 + 0.768220i \(0.721143\pi\)
\(570\) 0.469056 + 2.50941i 0.0196466 + 0.105107i
\(571\) 8.91516i 0.373088i 0.982447 + 0.186544i \(0.0597286\pi\)
−0.982447 + 0.186544i \(0.940271\pi\)
\(572\) 17.8658 + 7.91104i 0.747008 + 0.330777i
\(573\) 17.1442 17.1442i 0.716208 0.716208i
\(574\) −0.377485 0.101147i −0.0157559 0.00422178i
\(575\) −7.21751 + 5.27759i −0.300991 + 0.220091i
\(576\) −0.866025 0.500000i −0.0360844 0.0208333i
\(577\) 0.0200033i 0.000832749i −1.00000 0.000416374i \(-0.999867\pi\)
1.00000 0.000416374i \(-0.000132536\pi\)
\(578\) 2.71326 4.69950i 0.112857 0.195473i
\(579\) 24.1372 6.46754i 1.00311 0.268782i
\(580\) 2.89452 8.21372i 0.120188 0.341056i
\(581\) −0.169458 + 0.293510i −0.00703031 + 0.0121768i
\(582\) −13.4107 3.59338i −0.555890 0.148950i
\(583\) −36.4008 + 21.0160i −1.50757 + 0.870393i
\(584\) −11.8364 −0.489796
\(585\) −3.82177 + 7.09888i −0.158011 + 0.293502i
\(586\) 10.7133 0.442562
\(587\) −15.7733 + 9.10670i −0.651032 + 0.375874i −0.788852 0.614584i \(-0.789324\pi\)
0.137819 + 0.990457i \(0.455991\pi\)
\(588\) −6.75693 1.81051i −0.278651 0.0746643i
\(589\) 1.85084 3.20575i 0.0762625 0.132091i
\(590\) 11.4746 5.49463i 0.472402 0.226210i
\(591\) 6.79459 1.82061i 0.279492 0.0748897i
\(592\) −2.20233 + 3.81454i −0.0905151 + 0.156777i
\(593\) 25.0570i 1.02897i 0.857500 + 0.514483i \(0.172016\pi\)
−0.857500 + 0.514483i \(0.827984\pi\)
\(594\) 4.69312 + 2.70957i 0.192561 + 0.111175i
\(595\) 0.430782 + 0.295100i 0.0176603 + 0.0120979i
\(596\) −16.2235 4.34708i −0.664541 0.178063i
\(597\) −15.6843 + 15.6843i −0.641915 + 0.641915i
\(598\) 5.20853 3.80037i 0.212993 0.155409i
\(599\) 4.49917i 0.183831i 0.995767 + 0.0919155i \(0.0292990\pi\)
−0.995767 + 0.0919155i \(0.970701\pi\)
\(600\) −4.03609 + 2.95127i −0.164773 + 0.120485i
\(601\) −1.96296 3.39994i −0.0800706 0.138686i 0.823209 0.567738i \(-0.192181\pi\)
−0.903280 + 0.429051i \(0.858848\pi\)
\(602\) −0.157411 0.587467i −0.00641560 0.0239434i
\(603\) 1.03869 0.0422986
\(604\) −0.0827656 0.308886i −0.00336769 0.0125684i
\(605\) −26.7206 31.1892i −1.08635 1.26802i
\(606\) −3.87533 + 3.87533i −0.157424 + 0.157424i
\(607\) 30.3075 8.12088i 1.23014 0.329616i 0.415509 0.909589i \(-0.363603\pi\)
0.814636 + 0.579973i \(0.196937\pi\)
\(608\) 0.295488 1.10278i 0.0119836 0.0447234i
\(609\) 0.0691929 0.258232i 0.00280384 0.0104641i
\(610\) −5.76540 + 16.3603i −0.233434 + 0.662411i
\(611\) −12.3167 31.8927i −0.498280 1.29024i
\(612\) −2.40557 2.40557i −0.0972392 0.0972392i
\(613\) 11.6419 + 20.1643i 0.470211 + 0.814429i 0.999420 0.0340625i \(-0.0108445\pi\)
−0.529209 + 0.848492i \(0.677511\pi\)
\(614\) −16.0414 + 9.26151i −0.647378 + 0.373764i
\(615\) 9.66780 8.28265i 0.389843 0.333989i
\(616\) 0.263031 + 0.263031i 0.0105978 + 0.0105978i
\(617\) −27.2389 15.7264i −1.09659 0.633119i −0.161270 0.986910i \(-0.551559\pi\)
−0.935325 + 0.353791i \(0.884892\pi\)
\(618\) 1.19944 + 0.692499i 0.0482487 + 0.0278564i
\(619\) −28.3021 28.3021i −1.13756 1.13756i −0.988887 0.148669i \(-0.952501\pi\)
−0.148669 0.988887i \(-0.547499\pi\)
\(620\) 7.22855 + 0.557792i 0.290306 + 0.0224015i
\(621\) 1.54866 0.894121i 0.0621457 0.0358799i
\(622\) 1.48686 + 2.57533i 0.0596178 + 0.103261i
\(623\) 0.0103685 + 0.0103685i 0.000415407 + 0.000415407i
\(624\) 2.91265 2.12520i 0.116599 0.0850760i
\(625\) 5.34709 + 24.4215i 0.213883 + 0.976859i
\(626\) 3.54891 13.2447i 0.141843 0.529366i
\(627\) −1.60129 + 5.97610i −0.0639494 + 0.238662i
\(628\) −21.8678 + 5.85945i −0.872619 + 0.233817i
\(629\) −10.5957 + 10.5957i −0.422477 + 0.422477i
\(630\) −0.116561 + 0.0998611i −0.00464391 + 0.00397856i
\(631\) −7.93986 29.6319i −0.316081 1.17963i −0.922979 0.384850i \(-0.874253\pi\)
0.606899 0.794779i \(-0.292413\pi\)
\(632\) 11.5811 0.460673
\(633\) 5.22913 + 19.5154i 0.207839 + 0.775666i
\(634\) 3.22848 + 5.59190i 0.128219 + 0.222083i
\(635\) 19.5926 + 13.4216i 0.777507 + 0.532619i
\(636\) 7.75620i 0.307553i
\(637\) 15.8329 19.6332i 0.627322 0.777896i
\(638\) 14.9242 14.9242i 0.590853 0.590853i
\(639\) −5.00578 1.34130i −0.198026 0.0530608i
\(640\) 2.19800 0.410849i 0.0868836 0.0162402i
\(641\) 23.3183 + 13.4628i 0.921018 + 0.531750i 0.883960 0.467563i \(-0.154868\pi\)
0.0370580 + 0.999313i \(0.488201\pi\)
\(642\) 10.8239i 0.427184i
\(643\) 6.72252 11.6437i 0.265110 0.459185i −0.702482 0.711701i \(-0.747925\pi\)
0.967593 + 0.252517i \(0.0812583\pi\)
\(644\) 0.118566 0.0317698i 0.00467217 0.00125190i
\(645\) 18.6859 + 6.58493i 0.735757 + 0.259281i
\(646\) 1.94198 3.36361i 0.0764063 0.132340i
\(647\) 9.19569 + 2.46398i 0.361520 + 0.0968690i 0.435007 0.900427i \(-0.356746\pi\)
−0.0734867 + 0.997296i \(0.523413\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 30.8327 1.21029
\(650\) −3.83773 17.6145i −0.150528 0.690899i
\(651\) 0.222560 0.00872281
\(652\) 9.90998 5.72153i 0.388105 0.224072i
\(653\) −17.5352 4.69855i −0.686206 0.183868i −0.101162 0.994870i \(-0.532256\pi\)
−0.585044 + 0.811002i \(0.698923\pi\)
\(654\) 5.89719 10.2142i 0.230598 0.399408i
\(655\) 40.8946 + 14.4113i 1.59789 + 0.563096i
\(656\) −5.49931 + 1.47354i −0.214712 + 0.0575319i
\(657\) 5.91822 10.2507i 0.230892 0.399916i
\(658\) 0.650876i 0.0253738i
\(659\) −5.97168 3.44775i −0.232624 0.134305i 0.379158 0.925332i \(-0.376214\pi\)
−0.611782 + 0.791027i \(0.709547\pi\)
\(660\) −11.9113 + 2.22645i −0.463646 + 0.0866644i
\(661\) −23.7763 6.37085i −0.924792 0.247797i −0.235160 0.971957i \(-0.575561\pi\)
−0.689633 + 0.724159i \(0.742228\pi\)
\(662\) 14.3133 14.3133i 0.556303 0.556303i
\(663\) 11.4424 4.41895i 0.444386 0.171618i
\(664\) 4.93743i 0.191609i
\(665\) −0.144567 0.0990332i −0.00560606 0.00384034i
\(666\) −2.20233 3.81454i −0.0853384 0.147810i
\(667\) −1.80259 6.72736i −0.0697966 0.260484i
\(668\) −6.68794 −0.258764
\(669\) 4.71011 + 17.5784i 0.182103 + 0.679619i
\(670\) −1.76379 + 1.51109i −0.0681412 + 0.0583783i
\(671\) −29.7264 + 29.7264i −1.14758 + 1.14758i
\(672\) 0.0663033 0.0177659i 0.00255770 0.000685335i
\(673\) 4.96061 18.5132i 0.191217 0.713633i −0.801996 0.597329i \(-0.796229\pi\)
0.993214 0.116304i \(-0.0371047\pi\)
\(674\) −5.19914 + 19.4034i −0.200263 + 0.747392i
\(675\) −0.537829 4.97099i −0.0207011 0.191333i
\(676\) 2.75437 + 12.7049i 0.105937 + 0.488648i
\(677\) −13.3554 13.3554i −0.513291 0.513291i 0.402242 0.915533i \(-0.368231\pi\)
−0.915533 + 0.402242i \(0.868231\pi\)
\(678\) 10.0190 + 17.3534i 0.384778 + 0.666455i
\(679\) 0.825332 0.476505i 0.0316733 0.0182866i
\(680\) 7.58452 + 0.585260i 0.290853 + 0.0224437i
\(681\) −11.2262 11.2262i −0.430188 0.430188i
\(682\) 15.2166 + 8.78530i 0.582673 + 0.336406i
\(683\) 13.8583 + 8.00107i 0.530271 + 0.306152i 0.741127 0.671365i \(-0.234292\pi\)
−0.210856 + 0.977517i \(0.567625\pi\)
\(684\) 0.807288 + 0.807288i 0.0308674 + 0.0308674i
\(685\) −20.4323 + 17.5049i −0.780678 + 0.668827i
\(686\) 0.831963 0.480334i 0.0317645 0.0183392i
\(687\) 4.65014 + 8.05427i 0.177414 + 0.307290i
\(688\) −6.26518 6.26518i −0.238858 0.238858i
\(689\) −25.5706 11.3227i −0.974164 0.431362i
\(690\) −1.32901 + 3.77131i −0.0505946 + 0.143571i
\(691\) −9.59085 + 35.7936i −0.364853 + 1.36165i 0.502766 + 0.864422i \(0.332316\pi\)
−0.867620 + 0.497229i \(0.834351\pi\)
\(692\) 4.22203 15.7568i 0.160497 0.598984i
\(693\) −0.359307 + 0.0962761i −0.0136489 + 0.00365722i
\(694\) 19.8075 19.8075i 0.751884 0.751884i
\(695\) −6.33297 7.39207i −0.240223 0.280397i
\(696\) −1.00802 3.76199i −0.0382090 0.142598i
\(697\) −19.3685 −0.733635
\(698\) 5.33144 + 19.8972i 0.201798 + 0.753120i
\(699\) −11.7979 20.4346i −0.446239 0.772909i
\(700\) 0.0526543 0.339148i 0.00199015 0.0128186i
\(701\) 9.21330i 0.347982i 0.984747 + 0.173991i \(0.0556663\pi\)
−0.984747 + 0.173991i \(0.944334\pi\)
\(702\) 0.384149 + 3.58503i 0.0144988 + 0.135308i
\(703\) 3.55582 3.55582i 0.134110 0.134110i
\(704\) 5.23449 + 1.40258i 0.197282 + 0.0528616i
\(705\) 17.4921 + 11.9827i 0.658789 + 0.451293i
\(706\) −4.88014 2.81755i −0.183666 0.106040i
\(707\) 0.376197i 0.0141483i
\(708\) 2.84480 4.92733i 0.106914 0.185180i
\(709\) −41.8016 + 11.2007i −1.56989 + 0.420651i −0.935778 0.352590i \(-0.885301\pi\)
−0.634113 + 0.773241i \(0.718634\pi\)
\(710\) 10.4516 5.00479i 0.392243 0.187826i
\(711\) −5.79057 + 10.0296i −0.217163 + 0.376138i
\(712\) 0.206341 + 0.0552889i 0.00773295 + 0.00207204i
\(713\) 5.02126 2.89903i 0.188048 0.108569i
\(714\) 0.233520 0.00873925
\(715\) 10.0483 42.5193i 0.375786 1.59013i
\(716\) 15.4073 0.575798
\(717\) −16.9685 + 9.79675i −0.633699 + 0.365867i
\(718\) 9.42309 + 2.52491i 0.351667 + 0.0942288i
\(719\) −15.2449 + 26.4050i −0.568540 + 0.984741i 0.428170 + 0.903698i \(0.359158\pi\)
−0.996711 + 0.0810429i \(0.974175\pi\)
\(720\) −0.743195 + 2.10895i −0.0276972 + 0.0785959i
\(721\) −0.0918300 + 0.0246058i −0.00341993 + 0.000916367i
\(722\) 8.84829 15.3257i 0.329299 0.570363i
\(723\) 5.02860i 0.187016i
\(724\) −8.07491 4.66205i −0.300101 0.173264i
\(725\) −19.2430 2.98756i −0.714666 0.110955i
\(726\) −17.7413 4.75376i −0.658441 0.176429i
\(727\) 6.36716 6.36716i 0.236145 0.236145i −0.579107 0.815252i \(-0.696599\pi\)
0.815252 + 0.579107i \(0.196599\pi\)
\(728\) −0.0382210 + 0.244524i −0.00141656 + 0.00906266i
\(729\) 1.00000i 0.0370370i
\(730\) 4.86299 + 26.0165i 0.179987 + 0.962914i
\(731\) −15.0713 26.1042i −0.557432 0.965500i
\(732\) 2.00781 + 7.49325i 0.0742108 + 0.276959i
\(733\) 40.5199 1.49664 0.748319 0.663340i \(-0.230861\pi\)
0.748319 + 0.663340i \(0.230861\pi\)
\(734\) 2.70714 + 10.1032i 0.0999223 + 0.372915i
\(735\) −1.20343 + 15.5956i −0.0443894 + 0.575252i
\(736\) 1.26448 1.26448i 0.0466093 0.0466093i
\(737\) −5.43699 + 1.45684i −0.200274 + 0.0536633i
\(738\) 1.47354 5.49931i 0.0542416 0.202432i
\(739\) −3.56257 + 13.2957i −0.131051 + 0.489089i −0.999983 0.00584246i \(-0.998140\pi\)
0.868932 + 0.494932i \(0.164807\pi\)
\(740\) 9.28919 + 3.27352i 0.341477 + 0.120337i
\(741\) −3.83997 + 1.48296i −0.141065 + 0.0544780i
\(742\) −0.376466 0.376466i −0.0138205 0.0138205i
\(743\) −23.9312 41.4501i −0.877951 1.52065i −0.853586 0.520952i \(-0.825577\pi\)
−0.0243644 0.999703i \(-0.507756\pi\)
\(744\) 2.80793 1.62116i 0.102944 0.0594346i
\(745\) −2.88947 + 37.4453i −0.105862 + 1.37189i
\(746\) −4.65646 4.65646i −0.170485 0.170485i
\(747\) −4.27594 2.46871i −0.156448 0.0903256i
\(748\) 15.9659 + 9.21792i 0.583771 + 0.337041i
\(749\) 0.525362 + 0.525362i 0.0191963 + 0.0191963i
\(750\) 8.14511 + 7.65880i 0.297417 + 0.279660i
\(751\) 11.5401 6.66266i 0.421103 0.243124i −0.274446 0.961602i \(-0.588495\pi\)
0.695549 + 0.718479i \(0.255161\pi\)
\(752\) −4.74108 8.21179i −0.172889 0.299453i
\(753\) −19.5866 19.5866i −0.713775 0.713775i
\(754\) 13.8741 + 2.16863i 0.505264 + 0.0789767i
\(755\) −0.644926 + 0.308824i −0.0234713 + 0.0112393i
\(756\) −0.0177659 + 0.0663033i −0.000646140 + 0.00241143i
\(757\) −4.53887 + 16.9393i −0.164968 + 0.615668i 0.833076 + 0.553158i \(0.186577\pi\)
−0.998044 + 0.0625106i \(0.980089\pi\)
\(758\) 7.82771 2.09743i 0.284315 0.0761821i
\(759\) −6.85239 + 6.85239i −0.248726 + 0.248726i
\(760\) −2.54530 0.196408i −0.0923278 0.00712448i
\(761\) 10.9525 + 40.8753i 0.397028 + 1.48173i 0.818299 + 0.574793i \(0.194917\pi\)
−0.421271 + 0.906935i \(0.638416\pi\)
\(762\) 10.6208 0.384751
\(763\) 0.209538 + 0.782007i 0.00758579 + 0.0283105i
\(764\) 12.1228 + 20.9972i 0.438586 + 0.759653i
\(765\) −4.29911 + 6.27576i −0.155435 + 0.226900i
\(766\) 12.8545i 0.464450i
\(767\) 12.0915 + 16.5718i 0.436599 + 0.598373i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 23.4731 + 6.28959i 0.846460 + 0.226808i 0.655882 0.754864i \(-0.272297\pi\)
0.190578 + 0.981672i \(0.438964\pi\)
\(770\) 0.470076 0.686208i 0.0169404 0.0247292i
\(771\) −13.1581 7.59685i −0.473878 0.273594i
\(772\) 24.9887i 0.899361i
\(773\) 8.58044 14.8618i 0.308617 0.534540i −0.669443 0.742863i \(-0.733467\pi\)
0.978060 + 0.208323i \(0.0668005\pi\)
\(774\) 8.55839 2.29321i 0.307625 0.0824279i
\(775\) −1.74381 16.1175i −0.0626396 0.578959i
\(776\) 6.94187 12.0237i 0.249199 0.431625i
\(777\) 0.292043 + 0.0782527i 0.0104770 + 0.00280730i
\(778\) 33.0652 19.0902i 1.18545 0.684417i
\(779\) 6.49991 0.232884
\(780\) −5.86784 5.52887i −0.210102 0.197965i
\(781\) 28.0840 1.00492
\(782\) 5.26853 3.04179i 0.188402 0.108774i
\(783\) 3.76199 + 1.00802i 0.134443 + 0.0360238i
\(784\) 3.49764 6.05810i 0.124916 0.216361i
\(785\) 21.8634 + 45.6580i 0.780338 + 1.62960i
\(786\) 18.7303 5.01876i 0.668087 0.179013i
\(787\) 0.0836833 0.144944i 0.00298299 0.00516669i −0.864530 0.502581i \(-0.832384\pi\)
0.867513 + 0.497414i \(0.165717\pi\)
\(788\) 7.03428i 0.250586i
\(789\) 8.97093 + 5.17937i 0.319373 + 0.184390i
\(790\) −4.75810 25.4554i −0.169286 0.905661i
\(791\) −1.32859 0.355994i −0.0472391 0.0126577i
\(792\) −3.83191 + 3.83191i −0.136161 + 0.136161i
\(793\) −27.6348 4.31954i −0.981342 0.153391i
\(794\) 24.1221i 0.856062i
\(795\) 17.0481 3.18662i 0.604635 0.113018i
\(796\) −11.0905 19.2092i −0.393091 0.680854i
\(797\) −5.28534 19.7252i −0.187217 0.698702i −0.994145 0.108053i \(-0.965538\pi\)
0.806929 0.590649i \(-0.201128\pi\)
\(798\) −0.0783672 −0.00277417
\(799\) −8.34902 31.1590i −0.295367 1.10232i
\(800\) −1.80609 4.66241i −0.0638549 0.164841i
\(801\) −0.151052 + 0.151052i −0.00533716 + 0.00533716i
\(802\) 37.2272 9.97501i 1.31454 0.352230i
\(803\) −16.6015 + 61.9578i −0.585855 + 2.18644i
\(804\) −0.268832 + 1.00329i −0.00948096 + 0.0353834i
\(805\) −0.118543 0.247556i −0.00417808 0.00872521i
\(806\) 1.24553 + 11.6238i 0.0438720 + 0.409431i
\(807\) 2.63898 + 2.63898i 0.0928966 + 0.0928966i
\(808\) −2.74027 4.74629i −0.0964024 0.166974i
\(809\) −32.4615 + 18.7417i −1.14129 + 0.658922i −0.946749 0.321973i \(-0.895654\pi\)
−0.194537 + 0.980895i \(0.562321\pi\)
\(810\) −1.45481 1.69810i −0.0511166 0.0596651i
\(811\) 27.9343 + 27.9343i 0.980907 + 0.980907i 0.999821 0.0189136i \(-0.00602076\pi\)
−0.0189136 + 0.999821i \(0.506021\pi\)
\(812\) 0.231524 + 0.133670i 0.00812490 + 0.00469091i
\(813\) 13.3665 + 7.71718i 0.468785 + 0.270653i
\(814\) 16.8783 + 16.8783i 0.591582 + 0.591582i
\(815\) −16.6474 19.4314i −0.583134 0.680654i
\(816\) 2.94620 1.70099i 0.103138 0.0595466i
\(817\) 5.05780 + 8.76036i 0.176950 + 0.306486i
\(818\) 12.5628 + 12.5628i 0.439249 + 0.439249i
\(819\) −0.192653 0.155362i −0.00673186 0.00542880i
\(820\) 5.49821 + 11.4821i 0.192006 + 0.400972i
\(821\) −3.50998 + 13.0994i −0.122499 + 0.457173i −0.999738 0.0228809i \(-0.992716\pi\)
0.877239 + 0.480054i \(0.159383\pi\)
\(822\) −3.11423 + 11.6225i −0.108621 + 0.405380i
\(823\) −7.16885 + 1.92089i −0.249890 + 0.0669579i −0.381590 0.924332i \(-0.624623\pi\)
0.131699 + 0.991290i \(0.457957\pi\)
\(824\) −0.979342 + 0.979342i −0.0341170 + 0.0341170i
\(825\) 9.78746 + 25.2663i 0.340756 + 0.879658i
\(826\) 0.101081 + 0.377239i 0.00351705 + 0.0131258i
\(827\) 55.9023 1.94391 0.971957 0.235159i \(-0.0755611\pi\)
0.971957 + 0.235159i \(0.0755611\pi\)
\(828\) 0.462831 + 1.72731i 0.0160845 + 0.0600282i
\(829\) −16.1654 27.9992i −0.561446 0.972454i −0.997371 0.0724702i \(-0.976912\pi\)
0.435924 0.899983i \(-0.356422\pi\)
\(830\) 10.8525 2.02854i 0.376695 0.0704115i
\(831\) 25.3752i 0.880257i
\(832\) 1.29893 + 3.36345i 0.0450324 + 0.116607i
\(833\) 16.8276 16.8276i 0.583043 0.583043i
\(834\) −4.20481 1.12668i −0.145601 0.0390136i
\(835\) 2.74773 + 14.7001i 0.0950892 + 0.508718i
\(836\) −5.35802 3.09346i −0.185311 0.106989i
\(837\) 3.24232i 0.112071i
\(838\) −2.35976 + 4.08722i −0.0815165 + 0.141191i
\(839\) −5.89837 + 1.58046i −0.203634 + 0.0545637i −0.359194 0.933263i \(-0.616948\pi\)
0.155560 + 0.987826i \(0.450282\pi\)
\(840\) −0.0662901 0.138436i −0.00228723 0.00477648i
\(841\) −6.91565 + 11.9783i −0.238471 + 0.413043i
\(842\) −22.1464 5.93410i −0.763214 0.204503i
\(843\) 10.2068 5.89290i 0.351541 0.202962i
\(844\) −20.2038 −0.695443
\(845\) 26.7937 11.2739i 0.921730 0.387833i
\(846\) 9.48215 0.326003
\(847\) 1.09185 0.630380i 0.0375164 0.0216601i
\(848\) −7.49191 2.00745i −0.257273 0.0689362i
\(849\) −10.5814 + 18.3274i −0.363151 + 0.628996i
\(850\) −1.82969 16.9112i −0.0627577 0.580050i
\(851\) 7.60820 2.03861i 0.260806 0.0698827i
\(852\) 2.59118 4.48806i 0.0887725 0.153758i
\(853\) 47.1782i 1.61535i 0.589627 + 0.807676i \(0.299275\pi\)
−0.589627 + 0.807676i \(0.700725\pi\)
\(854\) −0.461157 0.266249i −0.0157805 0.00911085i
\(855\) 1.44275 2.10609i 0.0493408 0.0720268i
\(856\) 10.4550 + 2.80142i 0.357346 + 0.0957506i
\(857\) 27.1912 27.1912i 0.928835 0.928835i −0.0687960 0.997631i \(-0.521916\pi\)
0.997631 + 0.0687960i \(0.0219157\pi\)
\(858\) −7.03910 18.2270i −0.240311 0.622260i
\(859\) 37.8456i 1.29127i 0.763645 + 0.645637i \(0.223408\pi\)
−0.763645 + 0.645637i \(0.776592\pi\)
\(860\) −11.1968 + 16.3449i −0.381808 + 0.557356i
\(861\) 0.195400 + 0.338444i 0.00665923 + 0.0115341i
\(862\) −6.81996 25.4525i −0.232289 0.866914i
\(863\) 41.3242 1.40669 0.703346 0.710847i \(-0.251688\pi\)
0.703346 + 0.710847i \(0.251688\pi\)
\(864\) 0.258819 + 0.965926i 0.00880520 + 0.0328615i
\(865\) −36.3681 2.80635i −1.23655 0.0954187i
\(866\) −14.1765 + 14.1765i −0.481737 + 0.481737i
\(867\) −5.24161 + 1.40448i −0.178014 + 0.0476988i
\(868\) −0.0576027 + 0.214976i −0.00195516 + 0.00729677i
\(869\) 16.2435 60.6214i 0.551022 2.05644i
\(870\) −7.85471 + 3.76124i −0.266300 + 0.127518i
\(871\) −2.91521 2.35092i −0.0987781 0.0796580i
\(872\) 8.33989 + 8.33989i 0.282424 + 0.282424i
\(873\) 6.94187 + 12.0237i 0.234947 + 0.406940i
\(874\) −1.76807 + 1.02080i −0.0598060 + 0.0345290i
\(875\) −0.767080 + 0.0236043i −0.0259320 + 0.000797969i
\(876\) 8.36963 + 8.36963i 0.282784 + 0.282784i
\(877\) 23.2348 + 13.4146i 0.784583 + 0.452979i 0.838052 0.545590i \(-0.183694\pi\)
−0.0534688 + 0.998570i \(0.517028\pi\)
\(878\) 6.71707 + 3.87810i 0.226690 + 0.130880i
\(879\) −7.57544 7.57544i −0.255513 0.255513i
\(880\) 0.932283 12.0817i 0.0314272 0.407273i
\(881\) 19.8210 11.4437i 0.667788 0.385547i −0.127450 0.991845i \(-0.540679\pi\)
0.795238 + 0.606298i \(0.207346\pi\)
\(882\) 3.49764 + 6.05810i 0.117772 + 0.203987i
\(883\) −31.2334 31.2334i −1.05109 1.05109i −0.998623 0.0524655i \(-0.983292\pi\)
−0.0524655 0.998623i \(-0.516708\pi\)
\(884\) 1.30687 + 12.1962i 0.0439547 + 0.410203i
\(885\) −11.9991 4.22848i −0.403344 0.142139i
\(886\) −2.66419 + 9.94288i −0.0895051 + 0.334037i
\(887\) −12.6629 + 47.2584i −0.425177 + 1.58678i 0.338359 + 0.941017i \(0.390128\pi\)
−0.763536 + 0.645765i \(0.776539\pi\)
\(888\) 4.25457 1.14001i 0.142774 0.0382562i
\(889\) −0.515506 + 0.515506i −0.0172895 + 0.0172895i
\(890\) 0.0367501 0.476253i 0.00123187 0.0159640i
\(891\) −1.40258 5.23449i −0.0469881 0.175362i
\(892\) −18.1985 −0.609329
\(893\) 2.80186 + 10.4567i 0.0937607 + 0.349920i
\(894\) 8.39791 + 14.5456i 0.280868 + 0.486478i
\(895\) −6.33007 33.8653i −0.211591 1.13199i
\(896\) 0.0686422i 0.00229318i
\(897\) −6.37025 0.995720i −0.212697 0.0332461i
\(898\) 1.10366 1.10366i 0.0368297 0.0368297i
\(899\) 12.1976 + 3.26833i 0.406812 + 0.109005i
\(900\) 4.94081 + 0.767084i 0.164694 + 0.0255695i
\(901\) −22.8513 13.1932i −0.761289 0.439530i
\(902\) 30.8528i 1.02729i
\(903\) −0.304095 + 0.526708i −0.0101197 + 0.0175278i
\(904\) −19.3553 + 5.18622i −0.643746 + 0.172491i
\(905\) −6.92962 + 19.6640i −0.230348 + 0.653655i
\(906\) −0.159891 + 0.276939i −0.00531202 + 0.00920069i
\(907\) 35.4751 + 9.50552i 1.17793 + 0.315626i 0.794105 0.607780i \(-0.207940\pi\)
0.383825 + 0.923406i \(0.374606\pi\)
\(908\) 13.7492 7.93810i 0.456283 0.263435i
\(909\) 5.48054 0.181778
\(910\) 0.553167 0.0164526i 0.0183373 0.000545397i
\(911\) 26.2387 0.869326 0.434663 0.900593i \(-0.356867\pi\)
0.434663 + 0.900593i \(0.356867\pi\)
\(912\) −0.988721 + 0.570838i −0.0327398 + 0.0189024i
\(913\) 25.8449 + 6.92513i 0.855343 + 0.229188i
\(914\) −4.43984 + 7.69003i −0.146857 + 0.254364i
\(915\) 15.6453 7.49176i 0.517217 0.247670i
\(916\) −8.98337 + 2.40709i −0.296819 + 0.0795324i
\(917\) −0.665521 + 1.15272i −0.0219774 + 0.0380660i
\(918\) 3.40198i 0.112282i
\(919\) −41.4582 23.9359i −1.36758 0.789572i −0.376961 0.926229i \(-0.623031\pi\)
−0.990618 + 0.136657i \(0.956364\pi\)
\(920\) −3.29883 2.25981i −0.108759 0.0745039i
\(921\) 17.8919 + 4.79411i 0.589557 + 0.157971i
\(922\) 6.85392 6.85392i 0.225722 0.225722i
\(923\) 11.0136 + 15.0944i 0.362515 + 0.496839i
\(924\) 0.371982i 0.0122373i
\(925\) 3.37874 21.7625i 0.111092 0.715548i
\(926\) −0.187218 0.324272i −0.00615238 0.0106562i
\(927\) −0.358464 1.33781i −0.0117735 0.0439393i
\(928\) 3.89470 0.127850
\(929\) 7.65813 + 28.5805i 0.251255 + 0.937697i 0.970136 + 0.242563i \(0.0779881\pi\)
−0.718881 + 0.695134i \(0.755345\pi\)
\(930\) −4.71694 5.50578i −0.154675 0.180542i
\(931\) −5.64721 + 5.64721i −0.185080 + 0.185080i
\(932\) 22.7919 6.10707i 0.746573 0.200044i
\(933\) 0.769658 2.87240i 0.0251975 0.0940382i
\(934\) −10.3229 + 38.5254i −0.337774 + 1.26059i
\(935\) 13.7014 38.8802i 0.448084 1.27152i
\(936\) −3.56230 0.556815i −0.116437 0.0182001i
\(937\) −31.4410 31.4410i −1.02713 1.02713i −0.999622 0.0275105i \(-0.991242\pi\)
−0.0275105 0.999622i \(-0.508758\pi\)
\(938\) −0.0356489 0.0617456i −0.00116398 0.00201607i
\(939\) −11.8749 + 6.85597i −0.387523 + 0.223736i
\(940\) −16.1016 + 13.7947i −0.525178 + 0.449933i
\(941\) 7.89735 + 7.89735i 0.257446 + 0.257446i 0.824015 0.566568i \(-0.191729\pi\)
−0.566568 + 0.824015i \(0.691729\pi\)
\(942\) 19.6061 + 11.3196i 0.638801 + 0.368812i
\(943\) 8.81701 + 5.09050i 0.287121 + 0.165770i
\(944\) 4.02315 + 4.02315i 0.130942 + 0.130942i
\(945\) 0.153034 + 0.0118089i 0.00497819 + 0.000384142i
\(946\) −41.5824 + 24.0076i −1.35196 + 0.780555i
\(947\) −3.19383 5.53188i −0.103786 0.179762i 0.809456 0.587181i \(-0.199762\pi\)
−0.913241 + 0.407419i \(0.866429\pi\)
\(948\) −8.18911 8.18911i −0.265970 0.265970i
\(949\) −39.8113 + 15.3747i −1.29233 + 0.499085i
\(950\) 0.614027 + 5.67526i 0.0199217 + 0.184130i
\(951\) 1.67119 6.23695i 0.0541919 0.202247i
\(952\) −0.0604393 + 0.225563i −0.00195885 + 0.00731053i
\(953\) −3.48236 + 0.933097i −0.112805 + 0.0302260i −0.314780 0.949165i \(-0.601931\pi\)
0.201975 + 0.979391i \(0.435264\pi\)
\(954\) 5.48446 5.48446i 0.177566 0.177566i
\(955\) 41.1713 35.2725i 1.33227 1.14139i
\(956\) −5.07117 18.9259i −0.164013 0.612107i
\(957\) −21.1060 −0.682258
\(958\) −8.58585 32.0428i −0.277396 1.03526i
\(959\) −0.412967 0.715280i −0.0133354 0.0230976i
\(960\) −1.84473 1.26371i −0.0595385 0.0407860i
\(961\) 20.4874i 0.660883i
\(962\) −2.45258 + 15.6907i −0.0790742 + 0.505888i
\(963\) −7.65363 + 7.65363i −0.246635 + 0.246635i
\(964\) −4.85725 1.30150i −0.156442 0.0419184i
\(965\) 54.9251 10.2666i 1.76810 0.330492i
\(966\) −0.106304 0.0613745i −0.00342027 0.00197469i
\(967\) 35.8339i 1.15234i −0.817329 0.576171i \(-0.804546\pi\)
0.817329 0.576171i \(-0.195454\pi\)
\(968\) 9.18357 15.9064i 0.295171 0.511251i
\(969\) −3.75162 + 1.00524i −0.120519 + 0.0322931i
\(970\) −29.2801 10.3183i −0.940127 0.331301i
\(971\) 15.2263 26.3727i 0.488635 0.846340i −0.511280 0.859414i \(-0.670828\pi\)
0.999915 + 0.0130742i \(0.00416178\pi\)
\(972\) −0.965926 0.258819i −0.0309821 0.00830162i
\(973\) 0.258777 0.149405i 0.00829599 0.00478969i
\(974\) −16.8724 −0.540625
\(975\) −9.74167 + 15.1690i −0.311983 + 0.485798i
\(976\) −7.75759 −0.248314
\(977\) −4.39224 + 2.53586i −0.140520 + 0.0811293i −0.568612 0.822606i \(-0.692519\pi\)
0.428092 + 0.903735i \(0.359186\pi\)
\(978\) −11.0531 2.96168i −0.353441 0.0947041i
\(979\) 0.578818 1.00254i 0.0184991 0.0320414i
\(980\) −14.7527 5.19886i −0.471258 0.166072i
\(981\) −11.3925 + 3.05261i −0.363735 + 0.0974624i
\(982\) 19.2792 33.3926i 0.615225 1.06560i
\(983\) 36.6196i 1.16798i 0.811760 + 0.583991i \(0.198510\pi\)
−0.811760 + 0.583991i \(0.801490\pi\)
\(984\) 4.93055 + 2.84665i 0.157180 + 0.0907479i
\(985\) 15.4613 2.89002i 0.492639 0.0920838i
\(986\) 12.7982 + 3.42928i 0.407579 + 0.109210i
\(987\) −0.460239 + 0.460239i −0.0146496 + 0.0146496i
\(988\) −0.438574 4.09294i −0.0139529 0.130214i
\(989\) 15.8444i 0.503821i
\(990\) 9.99688 + 6.84821i 0.317722 + 0.217650i
\(991\) −26.4267 45.7723i −0.839470 1.45401i −0.890338 0.455300i \(-0.849532\pi\)
0.0508679 0.998705i \(-0.483801\pi\)
\(992\) 0.839174 + 3.13184i 0.0266438 + 0.0994360i
\(993\) −20.2421 −0.642363
\(994\) 0.0920695 + 0.343608i 0.00292027 + 0.0108986i
\(995\) −37.6654 + 32.2689i −1.19407 + 1.02299i
\(996\) 3.49129 3.49129i 0.110626 0.110626i
\(997\) 11.7665 3.15282i 0.372649 0.0998509i −0.0676339 0.997710i \(-0.521545\pi\)
0.440282 + 0.897859i \(0.354878\pi\)
\(998\) 4.56800 17.0480i 0.144597 0.539645i
\(999\) −1.14001 + 4.25457i −0.0360683 + 0.134609i
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 390.2.bd.c.37.1 32
5.3 odd 4 390.2.bn.c.193.6 yes 32
13.6 odd 12 390.2.bn.c.97.6 yes 32
65.58 even 12 inner 390.2.bd.c.253.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bd.c.37.1 32 1.1 even 1 trivial
390.2.bd.c.253.1 yes 32 65.58 even 12 inner
390.2.bn.c.97.6 yes 32 13.6 odd 12
390.2.bn.c.193.6 yes 32 5.3 odd 4