Properties

Label 370.2.o.c.201.1
Level $370$
Weight $2$
Character 370.201
Analytic conductor $2.954$
Analytic rank $0$
Dimension $24$
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] = [370,2,Mod(71,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.o (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 201.1
Character \(\chi\) \(=\) 370.201
Dual form 370.2.o.c.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{2} +(-2.67866 + 0.974954i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -2.85057 q^{6} +(-0.751904 + 4.26426i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.92657 - 3.29478i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{2} +(-2.67866 + 0.974954i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -2.85057 q^{6} +(-0.751904 + 4.26426i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.92657 - 3.29478i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.207621 - 0.359611i) q^{11} +(-2.67866 - 0.974954i) q^{12} +(-4.59538 - 3.85598i) q^{13} +(-2.16502 + 3.74993i) q^{14} +(0.494997 + 2.80727i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-5.52741 + 4.63805i) q^{17} +(4.81665 - 1.75312i) q^{18} +(-5.60681 + 2.04071i) q^{19} +(0.766044 - 0.642788i) q^{20} +(-2.14336 - 12.1556i) q^{21} +(-0.0721061 - 0.408934i) q^{22} +(-0.487860 + 0.844998i) q^{23} +(-2.18367 - 1.83231i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-2.99942 - 5.19515i) q^{26} +(-3.02984 + 5.24783i) q^{27} +(-3.31701 + 2.78330i) q^{28} +(1.94662 + 3.37164i) q^{29} +(-0.494997 + 2.80727i) q^{30} +4.56006 q^{31} +(-0.173648 + 0.984808i) q^{32} +(0.906751 + 0.760855i) q^{33} +(-6.78038 + 2.46786i) q^{34} +(4.06891 + 1.48096i) q^{35} +5.12577 q^{36} +(5.40971 - 2.78119i) q^{37} -5.96665 q^{38} +(16.0689 + 5.84859i) q^{39} +(0.939693 - 0.342020i) q^{40} +(3.78411 + 3.17525i) q^{41} +(2.14336 - 12.1556i) q^{42} +0.692688 q^{43} +(0.0721061 - 0.408934i) q^{44} +(-2.56289 - 4.43905i) q^{45} +(-0.747444 + 0.627180i) q^{46} +(-0.577895 + 1.00094i) q^{47} +(-1.42529 - 2.46867i) q^{48} +(-11.0407 - 4.01849i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(10.2842 - 17.8128i) q^{51} +(-1.04169 - 5.90770i) q^{52} +(1.05353 + 5.97484i) q^{53} +(-4.64198 + 3.89508i) q^{54} +(-0.390200 + 0.142021i) q^{55} +(-4.06891 + 1.48096i) q^{56} +(13.0292 - 10.9328i) q^{57} +(0.676053 + 3.83409i) q^{58} +(0.996903 + 5.65372i) q^{59} +(-1.42529 + 2.46867i) q^{60} +(-7.62204 - 6.39565i) q^{61} +(4.28506 + 1.55963i) q^{62} +(11.0974 + 19.2213i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.59538 + 3.85598i) q^{65} +(0.591840 + 1.02510i) q^{66} +(-1.91375 + 10.8534i) q^{67} -7.21553 q^{68} +(0.482978 - 2.73910i) q^{69} +(3.31701 + 2.78330i) q^{70} +(-4.24992 + 1.54684i) q^{71} +(4.81665 + 1.75312i) q^{72} +16.3406 q^{73} +(6.03469 - 0.763236i) q^{74} +2.85057 q^{75} +(-5.60681 - 2.04071i) q^{76} +(1.68958 - 0.614959i) q^{77} +(13.0995 + 10.9918i) q^{78} +(0.498245 - 2.82569i) q^{79} +1.00000 q^{80} +(0.329278 - 1.86743i) q^{81} +(2.46990 + 4.27800i) q^{82} +(9.44869 - 7.92839i) q^{83} +(6.17156 - 10.6894i) q^{84} +(3.60776 + 6.24883i) q^{85} +(0.650914 + 0.236913i) q^{86} +(-8.50153 - 7.13363i) q^{87} +(0.207621 - 0.359611i) q^{88} +(1.83553 + 10.4098i) q^{89} +(-0.890081 - 5.04790i) q^{90} +(19.8982 - 16.6966i) q^{91} +(-0.916876 + 0.333716i) q^{92} +(-12.2149 + 4.44585i) q^{93} +(-0.885386 + 0.742927i) q^{94} +(1.03610 + 5.87600i) q^{95} +(-0.494997 - 2.80727i) q^{96} +(-3.75971 + 6.51200i) q^{97} +(-9.00047 - 7.55229i) q^{98} +(-2.00008 - 0.727969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31} - 39 q^{33} - 21 q^{34} + 6 q^{35} + 54 q^{36} - 12 q^{37} - 36 q^{38} - 18 q^{39} + 27 q^{41} - 36 q^{42} - 24 q^{43} - 9 q^{44} - 27 q^{45} + 3 q^{46} - 6 q^{47} - 3 q^{48} - 27 q^{49} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 9 q^{54} + 9 q^{55} - 6 q^{56} - 27 q^{57} + 27 q^{58} + 51 q^{59} - 3 q^{60} - 3 q^{62} - 27 q^{63} - 12 q^{64} + 15 q^{66} - 18 q^{69} + 3 q^{70} - 66 q^{71} + 6 q^{72} + 42 q^{73} - 42 q^{74} + 6 q^{75} - 6 q^{76} + 69 q^{77} + 36 q^{78} - 30 q^{79} + 24 q^{80} - 90 q^{81} + 24 q^{82} + 57 q^{83} + 6 q^{84} - 6 q^{86} + 6 q^{87} + 15 q^{88} - 57 q^{89} + 6 q^{90} + 3 q^{91} + 15 q^{92} - 72 q^{93} + 3 q^{94} - 15 q^{95} - 3 q^{97} - 72 q^{98} + 63 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 + 0.342020i 0.664463 + 0.241845i
\(3\) −2.67866 + 0.974954i −1.54653 + 0.562890i −0.967600 0.252489i \(-0.918751\pi\)
−0.578927 + 0.815379i \(0.696529\pi\)
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) 0.173648 0.984808i 0.0776578 0.440419i
\(6\) −2.85057 −1.16374
\(7\) −0.751904 + 4.26426i −0.284193 + 1.61174i 0.423960 + 0.905681i \(0.360640\pi\)
−0.708153 + 0.706059i \(0.750472\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) 3.92657 3.29478i 1.30886 1.09826i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −0.207621 0.359611i −0.0626002 0.108427i 0.833027 0.553233i \(-0.186606\pi\)
−0.895627 + 0.444806i \(0.853273\pi\)
\(12\) −2.67866 0.974954i −0.773264 0.281445i
\(13\) −4.59538 3.85598i −1.27453 1.06946i −0.993974 0.109618i \(-0.965037\pi\)
−0.280554 0.959838i \(-0.590518\pi\)
\(14\) −2.16502 + 3.74993i −0.578627 + 1.00221i
\(15\) 0.494997 + 2.80727i 0.127808 + 0.724833i
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −5.52741 + 4.63805i −1.34059 + 1.12489i −0.359122 + 0.933291i \(0.616924\pi\)
−0.981473 + 0.191602i \(0.938632\pi\)
\(18\) 4.81665 1.75312i 1.13530 0.413214i
\(19\) −5.60681 + 2.04071i −1.28629 + 0.468172i −0.892508 0.451032i \(-0.851056\pi\)
−0.393783 + 0.919203i \(0.628834\pi\)
\(20\) 0.766044 0.642788i 0.171293 0.143732i
\(21\) −2.14336 12.1556i −0.467719 2.65257i
\(22\) −0.0721061 0.408934i −0.0153731 0.0871850i
\(23\) −0.487860 + 0.844998i −0.101726 + 0.176194i −0.912396 0.409309i \(-0.865770\pi\)
0.810670 + 0.585503i \(0.199103\pi\)
\(24\) −2.18367 1.83231i −0.445739 0.374019i
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) −2.99942 5.19515i −0.588234 1.01885i
\(27\) −3.02984 + 5.24783i −0.583093 + 1.00995i
\(28\) −3.31701 + 2.78330i −0.626855 + 0.525994i
\(29\) 1.94662 + 3.37164i 0.361478 + 0.626098i 0.988204 0.153141i \(-0.0489389\pi\)
−0.626726 + 0.779239i \(0.715606\pi\)
\(30\) −0.494997 + 2.80727i −0.0903737 + 0.512535i
\(31\) 4.56006 0.819012 0.409506 0.912308i \(-0.365701\pi\)
0.409506 + 0.912308i \(0.365701\pi\)
\(32\) −0.173648 + 0.984808i −0.0306970 + 0.174091i
\(33\) 0.906751 + 0.760855i 0.157845 + 0.132448i
\(34\) −6.78038 + 2.46786i −1.16283 + 0.423234i
\(35\) 4.06891 + 1.48096i 0.687771 + 0.250328i
\(36\) 5.12577 0.854296
\(37\) 5.40971 2.78119i 0.889351 0.457225i
\(38\) −5.96665 −0.967918
\(39\) 16.0689 + 5.84859i 2.57308 + 0.936524i
\(40\) 0.939693 0.342020i 0.148578 0.0540781i
\(41\) 3.78411 + 3.17525i 0.590979 + 0.495890i 0.888532 0.458815i \(-0.151726\pi\)
−0.297553 + 0.954705i \(0.596170\pi\)
\(42\) 2.14336 12.1556i 0.330727 1.87565i
\(43\) 0.692688 0.105634 0.0528170 0.998604i \(-0.483180\pi\)
0.0528170 + 0.998604i \(0.483180\pi\)
\(44\) 0.0721061 0.408934i 0.0108704 0.0616491i
\(45\) −2.56289 4.43905i −0.382053 0.661735i
\(46\) −0.747444 + 0.627180i −0.110205 + 0.0924727i
\(47\) −0.577895 + 1.00094i −0.0842946 + 0.146003i −0.905090 0.425219i \(-0.860197\pi\)
0.820796 + 0.571222i \(0.193530\pi\)
\(48\) −1.42529 2.46867i −0.205722 0.356322i
\(49\) −11.0407 4.01849i −1.57725 0.574070i
\(50\) −0.766044 0.642788i −0.108335 0.0909039i
\(51\) 10.2842 17.8128i 1.44008 2.49428i
\(52\) −1.04169 5.90770i −0.144456 0.819251i
\(53\) 1.05353 + 5.97484i 0.144713 + 0.820708i 0.967597 + 0.252499i \(0.0812524\pi\)
−0.822884 + 0.568209i \(0.807636\pi\)
\(54\) −4.64198 + 3.89508i −0.631694 + 0.530054i
\(55\) −0.390200 + 0.142021i −0.0526146 + 0.0191502i
\(56\) −4.06891 + 1.48096i −0.543731 + 0.197902i
\(57\) 13.0292 10.9328i 1.72575 1.44808i
\(58\) 0.676053 + 3.83409i 0.0887702 + 0.503441i
\(59\) 0.996903 + 5.65372i 0.129786 + 0.736051i 0.978350 + 0.206959i \(0.0663566\pi\)
−0.848564 + 0.529093i \(0.822532\pi\)
\(60\) −1.42529 + 2.46867i −0.184004 + 0.318704i
\(61\) −7.62204 6.39565i −0.975902 0.818879i 0.00756422 0.999971i \(-0.497592\pi\)
−0.983466 + 0.181093i \(0.942037\pi\)
\(62\) 4.28506 + 1.55963i 0.544203 + 0.198074i
\(63\) 11.0974 + 19.2213i 1.39814 + 2.42165i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) −4.59538 + 3.85598i −0.569986 + 0.478275i
\(66\) 0.591840 + 1.02510i 0.0728505 + 0.126181i
\(67\) −1.91375 + 10.8534i −0.233802 + 1.32596i 0.611320 + 0.791384i \(0.290639\pi\)
−0.845122 + 0.534574i \(0.820472\pi\)
\(68\) −7.21553 −0.875011
\(69\) 0.482978 2.73910i 0.0581437 0.329749i
\(70\) 3.31701 + 2.78330i 0.396458 + 0.332668i
\(71\) −4.24992 + 1.54684i −0.504373 + 0.183577i −0.581660 0.813432i \(-0.697596\pi\)
0.0772870 + 0.997009i \(0.475374\pi\)
\(72\) 4.81665 + 1.75312i 0.567648 + 0.206607i
\(73\) 16.3406 1.91253 0.956264 0.292506i \(-0.0944892\pi\)
0.956264 + 0.292506i \(0.0944892\pi\)
\(74\) 6.03469 0.763236i 0.701518 0.0887244i
\(75\) 2.85057 0.329156
\(76\) −5.60681 2.04071i −0.643146 0.234086i
\(77\) 1.68958 0.614959i 0.192546 0.0700810i
\(78\) 13.0995 + 10.9918i 1.48322 + 1.24457i
\(79\) 0.498245 2.82569i 0.0560570 0.317915i −0.943866 0.330329i \(-0.892840\pi\)
0.999923 + 0.0124138i \(0.00395154\pi\)
\(80\) 1.00000 0.111803
\(81\) 0.329278 1.86743i 0.0365864 0.207492i
\(82\) 2.46990 + 4.27800i 0.272755 + 0.472426i
\(83\) 9.44869 7.92839i 1.03713 0.870254i 0.0454468 0.998967i \(-0.485529\pi\)
0.991682 + 0.128712i \(0.0410844\pi\)
\(84\) 6.17156 10.6894i 0.673372 1.16631i
\(85\) 3.60776 + 6.24883i 0.391317 + 0.677781i
\(86\) 0.650914 + 0.236913i 0.0701899 + 0.0255470i
\(87\) −8.50153 7.13363i −0.911460 0.764806i
\(88\) 0.207621 0.359611i 0.0221325 0.0383346i
\(89\) 1.83553 + 10.4098i 0.194565 + 1.10344i 0.913036 + 0.407878i \(0.133731\pi\)
−0.718471 + 0.695557i \(0.755158\pi\)
\(90\) −0.890081 5.04790i −0.0938228 0.532096i
\(91\) 19.8982 16.6966i 2.08590 1.75027i
\(92\) −0.916876 + 0.333716i −0.0955909 + 0.0347923i
\(93\) −12.2149 + 4.44585i −1.26662 + 0.461013i
\(94\) −0.885386 + 0.742927i −0.0913206 + 0.0766271i
\(95\) 1.03610 + 5.87600i 0.106301 + 0.602865i
\(96\) −0.494997 2.80727i −0.0505204 0.286516i
\(97\) −3.75971 + 6.51200i −0.381740 + 0.661193i −0.991311 0.131538i \(-0.958008\pi\)
0.609571 + 0.792732i \(0.291342\pi\)
\(98\) −9.00047 7.55229i −0.909185 0.762897i
\(99\) −2.00008 0.727969i −0.201015 0.0731637i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −1.35568 + 2.34811i −0.134895 + 0.233645i −0.925557 0.378607i \(-0.876403\pi\)
0.790662 + 0.612253i \(0.209736\pi\)
\(102\) 15.7563 13.2211i 1.56011 1.30908i
\(103\) 4.34943 + 7.53343i 0.428562 + 0.742291i 0.996746 0.0806108i \(-0.0256871\pi\)
−0.568184 + 0.822902i \(0.692354\pi\)
\(104\) 1.04169 5.90770i 0.102146 0.579298i
\(105\) −12.3431 −1.20456
\(106\) −1.05353 + 5.97484i −0.102328 + 0.580328i
\(107\) −11.0401 9.26377i −1.06729 0.895562i −0.0724856 0.997369i \(-0.523093\pi\)
−0.994804 + 0.101807i \(0.967538\pi\)
\(108\) −5.69423 + 2.07253i −0.547928 + 0.199429i
\(109\) 8.50911 + 3.09706i 0.815025 + 0.296645i 0.715698 0.698410i \(-0.246109\pi\)
0.0993269 + 0.995055i \(0.468331\pi\)
\(110\) −0.415243 −0.0395918
\(111\) −11.7793 + 12.7241i −1.11804 + 1.20772i
\(112\) −4.33004 −0.409151
\(113\) −7.52374 2.73842i −0.707774 0.257609i −0.0370473 0.999314i \(-0.511795\pi\)
−0.670726 + 0.741705i \(0.734017\pi\)
\(114\) 15.9826 5.81720i 1.49691 0.544831i
\(115\) 0.747444 + 0.627180i 0.0696995 + 0.0584849i
\(116\) −0.676053 + 3.83409i −0.0627700 + 0.355986i
\(117\) −30.7487 −2.84272
\(118\) −0.996903 + 5.65372i −0.0917724 + 0.520467i
\(119\) −15.6218 27.0577i −1.43205 2.48038i
\(120\) −2.18367 + 1.83231i −0.199341 + 0.167267i
\(121\) 5.41379 9.37695i 0.492162 0.852450i
\(122\) −4.97493 8.61683i −0.450409 0.780131i
\(123\) −13.2321 4.81608i −1.19310 0.434252i
\(124\) 3.49321 + 2.93115i 0.313700 + 0.263225i
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 3.85409 + 21.8576i 0.343350 + 1.94723i
\(127\) 1.09433 + 6.20623i 0.0971057 + 0.550714i 0.994082 + 0.108635i \(0.0346478\pi\)
−0.896976 + 0.442079i \(0.854241\pi\)
\(128\) −0.766044 + 0.642788i −0.0677094 + 0.0568149i
\(129\) −1.85548 + 0.675339i −0.163366 + 0.0594603i
\(130\) −5.63706 + 2.05172i −0.494403 + 0.179948i
\(131\) −15.0481 + 12.6269i −1.31476 + 1.10322i −0.327374 + 0.944895i \(0.606164\pi\)
−0.987388 + 0.158321i \(0.949392\pi\)
\(132\) 0.205544 + 1.16570i 0.0178903 + 0.101461i
\(133\) −4.48635 25.4433i −0.389016 2.20622i
\(134\) −5.51043 + 9.54435i −0.476029 + 0.824506i
\(135\) 4.64198 + 3.89508i 0.399518 + 0.335235i
\(136\) −6.78038 2.46786i −0.581413 0.211617i
\(137\) −4.19202 7.26080i −0.358149 0.620332i 0.629503 0.776998i \(-0.283259\pi\)
−0.987652 + 0.156666i \(0.949925\pi\)
\(138\) 1.39068 2.40873i 0.118383 0.205045i
\(139\) 8.19778 6.87875i 0.695326 0.583448i −0.225113 0.974333i \(-0.572275\pi\)
0.920440 + 0.390885i \(0.127831\pi\)
\(140\) 2.16502 + 3.74993i 0.182978 + 0.316927i
\(141\) 0.572112 3.24461i 0.0481806 0.273245i
\(142\) −4.52267 −0.379534
\(143\) −0.432553 + 2.45313i −0.0361719 + 0.205141i
\(144\) 3.92657 + 3.29478i 0.327214 + 0.274565i
\(145\) 3.65845 1.33157i 0.303817 0.110580i
\(146\) 15.3552 + 5.58883i 1.27080 + 0.462535i
\(147\) 33.4922 2.76239
\(148\) 5.93179 + 1.34678i 0.487591 + 0.110704i
\(149\) 2.39548 0.196245 0.0981226 0.995174i \(-0.468716\pi\)
0.0981226 + 0.995174i \(0.468716\pi\)
\(150\) 2.67866 + 0.974954i 0.218712 + 0.0796046i
\(151\) −15.3264 + 5.57835i −1.24724 + 0.453960i −0.879470 0.475955i \(-0.842103\pi\)
−0.367775 + 0.929915i \(0.619880\pi\)
\(152\) −4.57072 3.83529i −0.370734 0.311083i
\(153\) −6.42240 + 36.4233i −0.519221 + 2.94465i
\(154\) 1.79802 0.144888
\(155\) 0.791847 4.49079i 0.0636027 0.360709i
\(156\) 8.55007 + 14.8091i 0.684553 + 1.18568i
\(157\) 12.4302 10.4302i 0.992039 0.832420i 0.00617765 0.999981i \(-0.498034\pi\)
0.985862 + 0.167561i \(0.0535891\pi\)
\(158\) 1.43464 2.48487i 0.114134 0.197686i
\(159\) −8.64724 14.9775i −0.685771 1.18779i
\(160\) 0.939693 + 0.342020i 0.0742892 + 0.0270391i
\(161\) −3.23647 2.71572i −0.255069 0.214029i
\(162\) 0.948117 1.64219i 0.0744911 0.129022i
\(163\) 0.617888 + 3.50422i 0.0483967 + 0.274471i 0.999397 0.0347182i \(-0.0110534\pi\)
−0.951000 + 0.309190i \(0.899942\pi\)
\(164\) 0.857788 + 4.86476i 0.0669820 + 0.379874i
\(165\) 0.906751 0.760855i 0.0705905 0.0592325i
\(166\) 11.5905 4.21861i 0.899600 0.327428i
\(167\) −6.37647 + 2.32084i −0.493426 + 0.179592i −0.576735 0.816931i \(-0.695673\pi\)
0.0833089 + 0.996524i \(0.473451\pi\)
\(168\) 9.45537 7.93400i 0.729498 0.612121i
\(169\) 3.99149 + 22.6368i 0.307037 + 1.74130i
\(170\) 1.25296 + 7.10591i 0.0960979 + 0.544998i
\(171\) −15.2918 + 26.4862i −1.16940 + 2.02545i
\(172\) 0.530630 + 0.445251i 0.0404601 + 0.0339501i
\(173\) −12.5193 4.55665i −0.951825 0.346436i −0.181000 0.983483i \(-0.557933\pi\)
−0.770825 + 0.637047i \(0.780156\pi\)
\(174\) −5.54898 9.61112i −0.420667 0.728617i
\(175\) 2.16502 3.74993i 0.163660 0.283468i
\(176\) 0.318094 0.266913i 0.0239773 0.0201193i
\(177\) −8.18248 14.1725i −0.615033 1.06527i
\(178\) −1.83553 + 10.4098i −0.137579 + 0.780247i
\(179\) 21.8885 1.63602 0.818012 0.575201i \(-0.195076\pi\)
0.818012 + 0.575201i \(0.195076\pi\)
\(180\) 0.890081 5.04790i 0.0663427 0.376248i
\(181\) 5.66838 + 4.75634i 0.421327 + 0.353536i 0.828668 0.559741i \(-0.189099\pi\)
−0.407340 + 0.913276i \(0.633544\pi\)
\(182\) 24.4087 8.88405i 1.80930 0.658530i
\(183\) 26.6523 + 9.70066i 1.97020 + 0.717093i
\(184\) −0.975719 −0.0719310
\(185\) −1.79955 5.81047i −0.132306 0.427195i
\(186\) −12.9988 −0.953118
\(187\) 2.81550 + 1.02476i 0.205890 + 0.0749378i
\(188\) −1.08609 + 0.395303i −0.0792110 + 0.0288305i
\(189\) −20.1000 16.8659i −1.46206 1.22681i
\(190\) −1.03610 + 5.87600i −0.0751664 + 0.426290i
\(191\) −8.88596 −0.642966 −0.321483 0.946915i \(-0.604181\pi\)
−0.321483 + 0.946915i \(0.604181\pi\)
\(192\) 0.494997 2.80727i 0.0357233 0.202597i
\(193\) −4.35202 7.53791i −0.313265 0.542591i 0.665802 0.746128i \(-0.268089\pi\)
−0.979067 + 0.203538i \(0.934756\pi\)
\(194\) −5.76020 + 4.83338i −0.413558 + 0.347017i
\(195\) 8.55007 14.8091i 0.612283 1.06051i
\(196\) −5.87464 10.1752i −0.419617 0.726799i
\(197\) 15.7540 + 5.73398i 1.12242 + 0.408529i 0.835537 0.549435i \(-0.185157\pi\)
0.286888 + 0.957964i \(0.407379\pi\)
\(198\) −1.63048 1.36813i −0.115873 0.0972291i
\(199\) 0.621096 1.07577i 0.0440283 0.0762593i −0.843171 0.537645i \(-0.819314\pi\)
0.887200 + 0.461385i \(0.152647\pi\)
\(200\) −0.173648 0.984808i −0.0122788 0.0696364i
\(201\) −5.45529 30.9385i −0.384787 2.18223i
\(202\) −2.07702 + 1.74283i −0.146139 + 0.122625i
\(203\) −15.8412 + 5.76574i −1.11184 + 0.404675i
\(204\) 19.3280 7.03481i 1.35323 0.492535i
\(205\) 3.78411 3.17525i 0.264294 0.221769i
\(206\) 1.51054 + 8.56670i 0.105244 + 0.596870i
\(207\) 0.868469 + 4.92533i 0.0603628 + 0.342334i
\(208\) 2.99942 5.19515i 0.207972 0.360219i
\(209\) 1.89796 + 1.59257i 0.131284 + 0.110161i
\(210\) −11.5987 4.22159i −0.800389 0.291318i
\(211\) −7.71904 13.3698i −0.531401 0.920413i −0.999328 0.0366462i \(-0.988333\pi\)
0.467928 0.883767i \(-0.345001\pi\)
\(212\) −3.03351 + 5.25419i −0.208342 + 0.360859i
\(213\) 9.87600 8.28695i 0.676693 0.567812i
\(214\) −7.20593 12.4810i −0.492588 0.853187i
\(215\) 0.120284 0.682165i 0.00820330 0.0465232i
\(216\) −6.05968 −0.412309
\(217\) −3.42873 + 19.4453i −0.232757 + 1.32003i
\(218\) 6.93669 + 5.82057i 0.469812 + 0.394219i
\(219\) −43.7711 + 15.9314i −2.95778 + 1.07654i
\(220\) −0.390200 0.142021i −0.0263073 0.00957508i
\(221\) 43.2848 2.91165
\(222\) −15.4208 + 7.92800i −1.03498 + 0.532092i
\(223\) −5.82315 −0.389947 −0.194974 0.980809i \(-0.562462\pi\)
−0.194974 + 0.980809i \(0.562462\pi\)
\(224\) −4.06891 1.48096i −0.271866 0.0989510i
\(225\) −4.81665 + 1.75312i −0.321110 + 0.116875i
\(226\) −6.13341 5.14654i −0.407988 0.342343i
\(227\) −2.35039 + 13.3297i −0.156001 + 0.884724i 0.801864 + 0.597506i \(0.203842\pi\)
−0.957865 + 0.287218i \(0.907270\pi\)
\(228\) 17.0084 1.12641
\(229\) 2.12525 12.0529i 0.140440 0.796476i −0.830476 0.557055i \(-0.811931\pi\)
0.970916 0.239421i \(-0.0769576\pi\)
\(230\) 0.487860 + 0.844998i 0.0321685 + 0.0557175i
\(231\) −3.92627 + 3.29453i −0.258330 + 0.216764i
\(232\) −1.94662 + 3.37164i −0.127802 + 0.221359i
\(233\) 1.58020 + 2.73698i 0.103522 + 0.179306i 0.913133 0.407661i \(-0.133655\pi\)
−0.809611 + 0.586966i \(0.800322\pi\)
\(234\) −28.8943 10.5167i −1.88888 0.687496i
\(235\) 0.885386 + 0.742927i 0.0577562 + 0.0484632i
\(236\) −2.87047 + 4.97180i −0.186852 + 0.323636i
\(237\) 1.42028 + 8.05484i 0.0922574 + 0.523218i
\(238\) −5.42539 30.7689i −0.351676 1.99445i
\(239\) −6.70944 + 5.62988i −0.433997 + 0.364167i −0.833458 0.552584i \(-0.813642\pi\)
0.399460 + 0.916751i \(0.369198\pi\)
\(240\) −2.67866 + 0.974954i −0.172907 + 0.0629330i
\(241\) 1.42330 0.518039i 0.0916828 0.0333698i −0.295772 0.955259i \(-0.595577\pi\)
0.387454 + 0.921889i \(0.373354\pi\)
\(242\) 8.29440 6.95983i 0.533184 0.447395i
\(243\) −2.21812 12.5796i −0.142293 0.806982i
\(244\) −1.72778 9.79870i −0.110609 0.627298i
\(245\) −5.87464 + 10.1752i −0.375317 + 0.650068i
\(246\) −10.7869 9.05127i −0.687747 0.577088i
\(247\) 33.6344 + 12.2419i 2.14010 + 0.778934i
\(248\) 2.28003 + 3.94913i 0.144782 + 0.250770i
\(249\) −17.5801 + 30.4495i −1.11409 + 1.92966i
\(250\) −0.766044 + 0.642788i −0.0484489 + 0.0406535i
\(251\) 6.47456 + 11.2143i 0.408671 + 0.707838i 0.994741 0.102422i \(-0.0326591\pi\)
−0.586070 + 0.810260i \(0.699326\pi\)
\(252\) −3.85409 + 21.8576i −0.242785 + 1.37690i
\(253\) 0.405160 0.0254722
\(254\) −1.09433 + 6.20623i −0.0686641 + 0.389413i
\(255\) −15.7563 13.2211i −0.986698 0.827938i
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −17.7906 6.47525i −1.10975 0.403915i −0.278846 0.960336i \(-0.589952\pi\)
−0.830901 + 0.556421i \(0.812174\pi\)
\(258\) −1.97456 −0.122931
\(259\) 7.79215 + 25.1596i 0.484180 + 1.56334i
\(260\) −5.99884 −0.372032
\(261\) 18.7524 + 6.82530i 1.16074 + 0.422476i
\(262\) −18.4593 + 6.71863i −1.14042 + 0.415078i
\(263\) 9.24067 + 7.75384i 0.569804 + 0.478123i 0.881581 0.472033i \(-0.156480\pi\)
−0.311777 + 0.950155i \(0.600924\pi\)
\(264\) −0.205544 + 1.16570i −0.0126503 + 0.0717437i
\(265\) 6.06702 0.372694
\(266\) 4.48635 25.4433i 0.275076 1.56003i
\(267\) −15.0658 26.0948i −0.922013 1.59697i
\(268\) −8.44247 + 7.08407i −0.515706 + 0.432729i
\(269\) −11.5687 + 20.0376i −0.705356 + 1.22171i 0.261208 + 0.965283i \(0.415879\pi\)
−0.966563 + 0.256429i \(0.917454\pi\)
\(270\) 3.02984 + 5.24783i 0.184390 + 0.319373i
\(271\) 4.63746 + 1.68790i 0.281705 + 0.102532i 0.479009 0.877810i \(-0.340996\pi\)
−0.197303 + 0.980342i \(0.563218\pi\)
\(272\) −5.52741 4.63805i −0.335149 0.281223i
\(273\) −37.0222 + 64.1243i −2.24068 + 3.88098i
\(274\) −1.45587 8.25667i −0.0879526 0.498804i
\(275\) 0.0721061 + 0.408934i 0.00434816 + 0.0246597i
\(276\) 2.13065 1.78782i 0.128250 0.107614i
\(277\) 4.48396 1.63203i 0.269415 0.0980590i −0.203780 0.979017i \(-0.565323\pi\)
0.473195 + 0.880958i \(0.343101\pi\)
\(278\) 10.0561 3.66011i 0.603122 0.219519i
\(279\) 17.9054 15.0244i 1.07197 0.899489i
\(280\) 0.751904 + 4.26426i 0.0449349 + 0.254838i
\(281\) 2.14496 + 12.1647i 0.127957 + 0.725682i 0.979507 + 0.201409i \(0.0645520\pi\)
−0.851550 + 0.524274i \(0.824337\pi\)
\(282\) 1.64733 2.85326i 0.0980972 0.169909i
\(283\) −19.1375 16.0583i −1.13761 0.954564i −0.138247 0.990398i \(-0.544147\pi\)
−0.999358 + 0.0358337i \(0.988591\pi\)
\(284\) −4.24992 1.54684i −0.252186 0.0917883i
\(285\) −8.50418 14.7297i −0.503744 0.872511i
\(286\) −1.24549 + 2.15725i −0.0736472 + 0.127561i
\(287\) −16.3854 + 13.7490i −0.967198 + 0.811575i
\(288\) 2.56289 + 4.43905i 0.151020 + 0.261574i
\(289\) 6.08877 34.5311i 0.358163 2.03124i
\(290\) 3.89324 0.228619
\(291\) 3.72209 21.1090i 0.218193 1.23743i
\(292\) 12.5177 + 10.5036i 0.732540 + 0.614674i
\(293\) 17.1812 6.25346i 1.00374 0.365331i 0.212714 0.977115i \(-0.431770\pi\)
0.791025 + 0.611783i \(0.209548\pi\)
\(294\) 31.4724 + 11.4550i 1.83551 + 0.668070i
\(295\) 5.74094 0.334250
\(296\) 5.11344 + 3.29435i 0.297213 + 0.191480i
\(297\) 2.51624 0.146007
\(298\) 2.25101 + 0.819301i 0.130398 + 0.0474609i
\(299\) 5.50019 2.00191i 0.318084 0.115773i
\(300\) 2.18367 + 1.83231i 0.126074 + 0.105789i
\(301\) −0.520835 + 2.95380i −0.0300204 + 0.170254i
\(302\) −16.3100 −0.938536
\(303\) 1.34212 7.61152i 0.0771025 0.437270i
\(304\) −2.98332 5.16727i −0.171105 0.296363i
\(305\) −7.62204 + 6.39565i −0.436437 + 0.366214i
\(306\) −18.4926 + 32.0301i −1.05715 + 1.83104i
\(307\) −3.10092 5.37095i −0.176979 0.306536i 0.763866 0.645375i \(-0.223299\pi\)
−0.940844 + 0.338839i \(0.889966\pi\)
\(308\) 1.68958 + 0.614959i 0.0962730 + 0.0350405i
\(309\) −18.9954 15.9390i −1.08061 0.906740i
\(310\) 2.28003 3.94913i 0.129497 0.224296i
\(311\) −3.98359 22.5921i −0.225889 1.28108i −0.860979 0.508641i \(-0.830148\pi\)
0.635090 0.772438i \(-0.280963\pi\)
\(312\) 2.96941 + 16.8403i 0.168110 + 0.953397i
\(313\) 15.3848 12.9094i 0.869602 0.729683i −0.0944122 0.995533i \(-0.530097\pi\)
0.964014 + 0.265850i \(0.0856527\pi\)
\(314\) 15.2479 5.54979i 0.860490 0.313193i
\(315\) 20.8563 7.59108i 1.17512 0.427709i
\(316\) 2.19800 1.84434i 0.123647 0.103752i
\(317\) −3.62517 20.5593i −0.203610 1.15473i −0.899613 0.436689i \(-0.856151\pi\)
0.696003 0.718039i \(-0.254960\pi\)
\(318\) −3.00316 17.0317i −0.168409 0.955092i
\(319\) 0.808319 1.40005i 0.0452572 0.0783877i
\(320\) 0.766044 + 0.642788i 0.0428232 + 0.0359329i
\(321\) 38.6045 + 14.0509i 2.15470 + 0.784245i
\(322\) −2.11245 3.65888i −0.117722 0.203901i
\(323\) 21.5262 37.2845i 1.19775 2.07457i
\(324\) 1.45260 1.21888i 0.0807000 0.0677153i
\(325\) 2.99942 + 5.19515i 0.166378 + 0.288175i
\(326\) −0.617888 + 3.50422i −0.0342216 + 0.194081i
\(327\) −25.8125 −1.42744
\(328\) −0.857788 + 4.86476i −0.0473634 + 0.268611i
\(329\) −3.83376 3.21691i −0.211362 0.177354i
\(330\) 1.11230 0.404842i 0.0612298 0.0222858i
\(331\) −28.5279 10.3833i −1.56803 0.570717i −0.595474 0.803374i \(-0.703036\pi\)
−0.972559 + 0.232657i \(0.925258\pi\)
\(332\) 12.3344 0.676938
\(333\) 12.0782 28.7444i 0.661880 1.57518i
\(334\) −6.78570 −0.371297
\(335\) 10.3562 + 3.76936i 0.565821 + 0.205942i
\(336\) 11.5987 4.22159i 0.632763 0.230307i
\(337\) 5.44504 + 4.56893i 0.296610 + 0.248886i 0.778932 0.627109i \(-0.215762\pi\)
−0.482321 + 0.875994i \(0.660206\pi\)
\(338\) −3.99149 + 22.6368i −0.217108 + 1.23128i
\(339\) 22.8234 1.23960
\(340\) −1.25296 + 7.10591i −0.0679515 + 0.385372i
\(341\) −0.946766 1.63985i −0.0512703 0.0888027i
\(342\) −23.4285 + 19.6588i −1.26687 + 1.06303i
\(343\) 10.2823 17.8095i 0.555192 0.961621i
\(344\) 0.346344 + 0.599886i 0.0186736 + 0.0323437i
\(345\) −2.61362 0.951281i −0.140713 0.0512153i
\(346\) −10.2058 8.56371i −0.548669 0.460388i
\(347\) −16.9490 + 29.3565i −0.909869 + 1.57594i −0.0956250 + 0.995417i \(0.530485\pi\)
−0.814244 + 0.580522i \(0.802848\pi\)
\(348\) −1.92714 10.9294i −0.103306 0.585875i
\(349\) 4.51198 + 25.5887i 0.241521 + 1.36973i 0.828436 + 0.560084i \(0.189231\pi\)
−0.586915 + 0.809649i \(0.699658\pi\)
\(350\) 3.31701 2.78330i 0.177301 0.148774i
\(351\) 34.1588 12.4328i 1.82326 0.663613i
\(352\) 0.390200 0.142021i 0.0207977 0.00756976i
\(353\) −19.5861 + 16.4347i −1.04246 + 0.874731i −0.992281 0.124009i \(-0.960425\pi\)
−0.0501830 + 0.998740i \(0.515980\pi\)
\(354\) −2.84175 16.1163i −0.151037 0.856574i
\(355\) 0.785353 + 4.45396i 0.0416822 + 0.236392i
\(356\) −5.28519 + 9.15421i −0.280114 + 0.485172i
\(357\) 68.2255 + 57.2480i 3.61088 + 3.02988i
\(358\) 20.5685 + 7.48631i 1.08708 + 0.395664i
\(359\) 8.64667 + 14.9765i 0.456354 + 0.790428i 0.998765 0.0496854i \(-0.0158219\pi\)
−0.542411 + 0.840113i \(0.682489\pi\)
\(360\) 2.56289 4.43905i 0.135076 0.233958i
\(361\) 12.7170 10.6708i 0.669316 0.561622i
\(362\) 3.69977 + 6.40819i 0.194456 + 0.336807i
\(363\) −5.35962 + 30.3959i −0.281307 + 1.59537i
\(364\) 25.9752 1.36147
\(365\) 2.83752 16.0924i 0.148523 0.842314i
\(366\) 21.7272 + 18.2313i 1.13570 + 0.952964i
\(367\) 18.1290 6.59842i 0.946327 0.344435i 0.177665 0.984091i \(-0.443146\pi\)
0.768661 + 0.639656i \(0.220923\pi\)
\(368\) −0.916876 0.333716i −0.0477955 0.0173961i
\(369\) 25.3203 1.31812
\(370\) 0.296272 6.07554i 0.0154024 0.315852i
\(371\) −26.2705 −1.36389
\(372\) −12.2149 4.44585i −0.633312 0.230507i
\(373\) −8.88915 + 3.23539i −0.460263 + 0.167522i −0.561736 0.827316i \(-0.689866\pi\)
0.101474 + 0.994838i \(0.467644\pi\)
\(374\) 2.29522 + 1.92592i 0.118683 + 0.0995868i
\(375\) 0.494997 2.80727i 0.0255615 0.144967i
\(376\) −1.15579 −0.0596053
\(377\) 4.05554 23.0001i 0.208871 1.18456i
\(378\) −13.1193 22.7234i −0.674786 1.16876i
\(379\) 0.823150 0.690705i 0.0422824 0.0354791i −0.621402 0.783492i \(-0.713436\pi\)
0.663684 + 0.748013i \(0.268992\pi\)
\(380\) −2.98332 + 5.16727i −0.153041 + 0.265075i
\(381\) −8.98211 15.5575i −0.460168 0.797034i
\(382\) −8.35007 3.03918i −0.427227 0.155498i
\(383\) 5.35821 + 4.49607i 0.273792 + 0.229739i 0.769336 0.638844i \(-0.220587\pi\)
−0.495545 + 0.868583i \(0.665031\pi\)
\(384\) 1.42529 2.46867i 0.0727339 0.125979i
\(385\) −0.312223 1.77070i −0.0159123 0.0902434i
\(386\) −1.51144 8.57180i −0.0769302 0.436293i
\(387\) 2.71989 2.28226i 0.138260 0.116014i
\(388\) −7.06593 + 2.57179i −0.358718 + 0.130563i
\(389\) −11.5807 + 4.21504i −0.587166 + 0.213711i −0.618483 0.785798i \(-0.712252\pi\)
0.0313164 + 0.999510i \(0.490030\pi\)
\(390\) 13.0995 10.9918i 0.663317 0.556589i
\(391\) −1.22254 6.93337i −0.0618265 0.350636i
\(392\) −2.04024 11.5708i −0.103048 0.584413i
\(393\) 27.9983 48.4944i 1.41233 2.44622i
\(394\) 12.8428 + 10.7764i 0.647009 + 0.542905i
\(395\) −2.69624 0.981351i −0.135663 0.0493771i
\(396\) −1.06422 1.84328i −0.0534791 0.0926284i
\(397\) 1.37147 2.37545i 0.0688320 0.119220i −0.829555 0.558424i \(-0.811406\pi\)
0.898387 + 0.439204i \(0.144739\pi\)
\(398\) 0.951574 0.798466i 0.0476981 0.0400235i
\(399\) 36.8235 + 63.7802i 1.84348 + 3.19300i
\(400\) 0.173648 0.984808i 0.00868241 0.0492404i
\(401\) 37.0770 1.85154 0.925768 0.378092i \(-0.123420\pi\)
0.925768 + 0.378092i \(0.123420\pi\)
\(402\) 5.45529 30.9385i 0.272085 1.54307i
\(403\) −20.9552 17.5835i −1.04385 0.875897i
\(404\) −2.54785 + 0.927340i −0.126760 + 0.0461369i
\(405\) −1.78188 0.648550i −0.0885422 0.0322267i
\(406\) −16.8579 −0.836643
\(407\) −2.12332 1.36795i −0.105249 0.0678070i
\(408\) 20.5684 1.01829
\(409\) −17.5278 6.37960i −0.866694 0.315451i −0.129866 0.991532i \(-0.541455\pi\)
−0.736828 + 0.676081i \(0.763677\pi\)
\(410\) 4.64190 1.68951i 0.229247 0.0834391i
\(411\) 18.3080 + 15.3622i 0.903065 + 0.757762i
\(412\) −1.51054 + 8.56670i −0.0744190 + 0.422051i
\(413\) −24.8585 −1.22321
\(414\) −0.868469 + 4.92533i −0.0426829 + 0.242067i
\(415\) −6.16720 10.6819i −0.302736 0.524354i
\(416\) 4.59538 3.85598i 0.225307 0.189055i
\(417\) −15.2526 + 26.4183i −0.746924 + 1.29371i
\(418\) 1.23880 + 2.14567i 0.0605918 + 0.104948i
\(419\) 13.6430 + 4.96564i 0.666504 + 0.242587i 0.653042 0.757322i \(-0.273493\pi\)
0.0134619 + 0.999909i \(0.495715\pi\)
\(420\) −9.45537 7.93400i −0.461375 0.387140i
\(421\) −16.8467 + 29.1793i −0.821058 + 1.42211i 0.0838376 + 0.996479i \(0.473282\pi\)
−0.904895 + 0.425634i \(0.860051\pi\)
\(422\) −2.68079 15.2035i −0.130499 0.740097i
\(423\) 1.02875 + 5.83431i 0.0500194 + 0.283674i
\(424\) −4.64760 + 3.89980i −0.225708 + 0.189391i
\(425\) 6.78038 2.46786i 0.328897 0.119709i
\(426\) 12.1147 4.40939i 0.586960 0.213636i
\(427\) 33.0038 27.6934i 1.59716 1.34018i
\(428\) −2.50259 14.1929i −0.120967 0.686041i
\(429\) −1.23302 6.99283i −0.0595310 0.337617i
\(430\) 0.346344 0.599886i 0.0167022 0.0289290i
\(431\) 6.35854 + 5.33545i 0.306280 + 0.256999i 0.782952 0.622082i \(-0.213713\pi\)
−0.476672 + 0.879081i \(0.658157\pi\)
\(432\) −5.69423 2.07253i −0.273964 0.0997147i
\(433\) −1.15839 2.00638i −0.0556685 0.0964207i 0.836848 0.547435i \(-0.184396\pi\)
−0.892517 + 0.451014i \(0.851062\pi\)
\(434\) −9.87264 + 17.0999i −0.473902 + 0.820822i
\(435\) −8.50153 + 7.13363i −0.407617 + 0.342031i
\(436\) 4.52760 + 7.84204i 0.216833 + 0.375565i
\(437\) 1.01094 5.73332i 0.0483598 0.274262i
\(438\) −46.5802 −2.22569
\(439\) −2.16184 + 12.2604i −0.103179 + 0.585156i 0.888753 + 0.458386i \(0.151572\pi\)
−0.991932 + 0.126770i \(0.959539\pi\)
\(440\) −0.318094 0.266913i −0.0151645 0.0127246i
\(441\) −56.5922 + 20.5979i −2.69487 + 0.980851i
\(442\) 40.6744 + 14.8043i 1.93468 + 0.704167i
\(443\) −5.64535 −0.268219 −0.134109 0.990967i \(-0.542817\pi\)
−0.134109 + 0.990967i \(0.542817\pi\)
\(444\) −17.2023 + 2.17566i −0.816386 + 0.103252i
\(445\) 10.5704 0.501084
\(446\) −5.47197 1.99164i −0.259105 0.0943067i
\(447\) −6.41668 + 2.33548i −0.303498 + 0.110464i
\(448\) −3.31701 2.78330i −0.156714 0.131499i
\(449\) −4.80382 + 27.2438i −0.226706 + 1.28572i 0.632690 + 0.774406i \(0.281951\pi\)
−0.859396 + 0.511311i \(0.829160\pi\)
\(450\) −5.12577 −0.241631
\(451\) 0.356190 2.02005i 0.0167723 0.0951207i
\(452\) −4.00330 6.93391i −0.188299 0.326144i
\(453\) 35.6156 29.8851i 1.67337 1.40412i
\(454\) −6.76767 + 11.7220i −0.317623 + 0.550138i
\(455\) −12.9876 22.4952i −0.608869 1.05459i
\(456\) 15.9826 + 5.81720i 0.748456 + 0.272416i
\(457\) 0.429818 + 0.360660i 0.0201060 + 0.0168710i 0.652785 0.757543i \(-0.273600\pi\)
−0.632679 + 0.774414i \(0.718045\pi\)
\(458\) 6.11940 10.5991i 0.285941 0.495264i
\(459\) −7.59255 43.0595i −0.354390 2.00984i
\(460\) 0.169432 + 0.960896i 0.00789980 + 0.0448020i
\(461\) 1.95360 1.63926i 0.0909880 0.0763480i −0.596159 0.802866i \(-0.703307\pi\)
0.687147 + 0.726518i \(0.258863\pi\)
\(462\) −4.81629 + 1.75299i −0.224074 + 0.0815563i
\(463\) 20.2159 7.35799i 0.939513 0.341955i 0.173540 0.984827i \(-0.444480\pi\)
0.765974 + 0.642872i \(0.222257\pi\)
\(464\) −2.98239 + 2.50252i −0.138454 + 0.116177i
\(465\) 2.25722 + 12.8013i 0.104676 + 0.593647i
\(466\) 0.548797 + 3.11238i 0.0254225 + 0.144178i
\(467\) −11.8537 + 20.5312i −0.548524 + 0.950071i 0.449852 + 0.893103i \(0.351477\pi\)
−0.998376 + 0.0569678i \(0.981857\pi\)
\(468\) −23.5549 19.7649i −1.08882 0.913632i
\(469\) −44.8429 16.3215i −2.07065 0.753656i
\(470\) 0.577895 + 1.00094i 0.0266563 + 0.0461701i
\(471\) −23.1274 + 40.0579i −1.06566 + 1.84577i
\(472\) −4.39781 + 3.69020i −0.202426 + 0.169855i
\(473\) −0.143817 0.249098i −0.00661270 0.0114535i
\(474\) −1.42028 + 8.05484i −0.0652358 + 0.369971i
\(475\) 5.96665 0.273768
\(476\) 5.42539 30.7689i 0.248672 1.41029i
\(477\) 23.8226 + 19.9895i 1.09076 + 0.915257i
\(478\) −8.23034 + 2.99560i −0.376447 + 0.137016i
\(479\) −24.4268 8.89063i −1.11609 0.406223i −0.282866 0.959159i \(-0.591285\pi\)
−0.833224 + 0.552936i \(0.813507\pi\)
\(480\) −2.85057 −0.130110
\(481\) −35.5839 8.07910i −1.62249 0.368375i
\(482\) 1.51464 0.0689901
\(483\) 11.3171 + 4.11909i 0.514946 + 0.187425i
\(484\) 10.1746 3.70325i 0.462481 0.168329i
\(485\) 5.76020 + 4.83338i 0.261557 + 0.219473i
\(486\) 2.21812 12.5796i 0.100616 0.570623i
\(487\) −1.43650 −0.0650943 −0.0325471 0.999470i \(-0.510362\pi\)
−0.0325471 + 0.999470i \(0.510362\pi\)
\(488\) 1.72778 9.79870i 0.0782127 0.443566i
\(489\) −5.07156 8.78420i −0.229344 0.397235i
\(490\) −9.00047 + 7.55229i −0.406600 + 0.341178i
\(491\) −11.9759 + 20.7429i −0.540467 + 0.936116i 0.458410 + 0.888741i \(0.348419\pi\)
−0.998877 + 0.0473753i \(0.984914\pi\)
\(492\) −7.04064 12.1947i −0.317417 0.549782i
\(493\) −26.3976 9.60795i −1.18889 0.432720i
\(494\) 27.4190 + 23.0073i 1.23364 + 1.03515i
\(495\) −1.06422 + 1.84328i −0.0478331 + 0.0828494i
\(496\) 0.791847 + 4.49079i 0.0355550 + 0.201642i
\(497\) −3.40062 19.2858i −0.152538 0.865088i
\(498\) −26.9342 + 22.6005i −1.20695 + 1.01275i
\(499\) 38.7514 14.1043i 1.73475 0.631397i 0.735799 0.677200i \(-0.236807\pi\)
0.998950 + 0.0458035i \(0.0145848\pi\)
\(500\) −0.939693 + 0.342020i −0.0420243 + 0.0152956i
\(501\) 14.8177 12.4335i 0.662006 0.555489i
\(502\) 2.24859 + 12.7524i 0.100360 + 0.569167i
\(503\) 4.12000 + 23.3657i 0.183702 + 1.04182i 0.927612 + 0.373545i \(0.121858\pi\)
−0.743910 + 0.668280i \(0.767031\pi\)
\(504\) −11.0974 + 19.2213i −0.494318 + 0.856184i
\(505\) 2.07702 + 1.74283i 0.0924263 + 0.0775549i
\(506\) 0.380726 + 0.138573i 0.0169253 + 0.00616032i
\(507\) −32.7617 56.7450i −1.45500 2.52013i
\(508\) −3.15098 + 5.45766i −0.139802 + 0.242145i
\(509\) 17.7178 14.8670i 0.785329 0.658969i −0.159255 0.987237i \(-0.550909\pi\)
0.944585 + 0.328268i \(0.106465\pi\)
\(510\) −10.2842 17.8128i −0.455392 0.788762i
\(511\) −12.2866 + 69.6808i −0.543527 + 3.08250i
\(512\) −1.00000 −0.0441942
\(513\) 6.27841 35.6066i 0.277199 1.57207i
\(514\) −14.5030 12.1695i −0.639701 0.536773i
\(515\) 8.17425 2.97518i 0.360200 0.131102i
\(516\) −1.85548 0.675339i −0.0816829 0.0297301i
\(517\) 0.479933 0.0211074
\(518\) −1.28287 + 26.3074i −0.0563661 + 1.15588i
\(519\) 37.9775 1.66703
\(520\) −5.63706 2.05172i −0.247202 0.0899740i
\(521\) 8.56733 3.11825i 0.375341 0.136613i −0.147459 0.989068i \(-0.547109\pi\)
0.522800 + 0.852455i \(0.324887\pi\)
\(522\) 15.2871 + 12.8274i 0.669097 + 0.561439i
\(523\) 2.17413 12.3301i 0.0950683 0.539159i −0.899658 0.436595i \(-0.856184\pi\)
0.994726 0.102564i \(-0.0327046\pi\)
\(524\) −19.6439 −0.858150
\(525\) −2.14336 + 12.1556i −0.0935439 + 0.530514i
\(526\) 6.03142 + 10.4467i 0.262982 + 0.455499i
\(527\) −25.2054 + 21.1498i −1.09796 + 0.921300i
\(528\) −0.591840 + 1.02510i −0.0257565 + 0.0446116i
\(529\) 11.0240 + 19.0941i 0.479304 + 0.830178i
\(530\) 5.70113 + 2.07504i 0.247641 + 0.0901341i
\(531\) 22.5422 + 18.9151i 0.978248 + 0.820847i
\(532\) 12.9179 22.3745i 0.560063 0.970057i
\(533\) −5.14573 29.1829i −0.222886 1.26405i
\(534\) −5.23230 29.6739i −0.226424 1.28411i
\(535\) −11.0401 + 9.26377i −0.477306 + 0.400508i
\(536\) −10.3562 + 3.76936i −0.447321 + 0.162811i
\(537\) −58.6319 + 21.3403i −2.53015 + 0.920901i
\(538\) −17.7243 + 14.8724i −0.764147 + 0.641196i
\(539\) 0.847195 + 4.80468i 0.0364913 + 0.206952i
\(540\) 1.05225 + 5.96762i 0.0452817 + 0.256805i
\(541\) −11.1639 + 19.3365i −0.479975 + 0.831342i −0.999736 0.0229702i \(-0.992688\pi\)
0.519761 + 0.854312i \(0.326021\pi\)
\(542\) 3.78049 + 3.17221i 0.162386 + 0.136258i
\(543\) −19.8209 7.21421i −0.850596 0.309592i
\(544\) −3.60776 6.24883i −0.154682 0.267916i
\(545\) 4.52760 7.84204i 0.193941 0.335916i
\(546\) −56.7213 + 47.5948i −2.42745 + 2.03687i
\(547\) −22.8839 39.6360i −0.978443 1.69471i −0.668070 0.744098i \(-0.732880\pi\)
−0.310373 0.950615i \(-0.600454\pi\)
\(548\) 1.45587 8.25667i 0.0621919 0.352708i
\(549\) −51.0007 −2.17666
\(550\) −0.0721061 + 0.408934i −0.00307462 + 0.0174370i
\(551\) −17.7949 14.9317i −0.758087 0.636111i
\(552\) 2.61362 0.951281i 0.111243 0.0404892i
\(553\) 11.6748 + 4.24930i 0.496465 + 0.180698i
\(554\) 4.77173 0.202731
\(555\) 10.4853 + 13.8098i 0.445078 + 0.586194i
\(556\) 10.7014 0.453842
\(557\) −2.11989 0.771576i −0.0898225 0.0326927i 0.296718 0.954965i \(-0.404108\pi\)
−0.386541 + 0.922272i \(0.626330\pi\)
\(558\) 21.9642 7.99433i 0.929820 0.338427i
\(559\) −3.18316 2.67099i −0.134633 0.112971i
\(560\) −0.751904 + 4.26426i −0.0317738 + 0.180198i
\(561\) −8.54087 −0.360596
\(562\) −2.14496 + 12.1647i −0.0904795 + 0.513135i
\(563\) −0.633638 1.09749i −0.0267047 0.0462538i 0.852364 0.522949i \(-0.175168\pi\)
−0.879069 + 0.476695i \(0.841835\pi\)
\(564\) 2.52386 2.11777i 0.106274 0.0891742i
\(565\) −4.00330 + 6.93391i −0.168420 + 0.291712i
\(566\) −12.4911 21.6352i −0.525040 0.909396i
\(567\) 7.71561 + 2.80825i 0.324025 + 0.117935i
\(568\) −3.46457 2.90712i −0.145370 0.121980i
\(569\) −6.58762 + 11.4101i −0.276167 + 0.478336i −0.970429 0.241387i \(-0.922398\pi\)
0.694262 + 0.719723i \(0.255731\pi\)
\(570\) −2.95347 16.7500i −0.123707 0.701579i
\(571\) −1.36567 7.74512i −0.0571516 0.324123i 0.942806 0.333342i \(-0.108176\pi\)
−0.999958 + 0.00921931i \(0.997065\pi\)
\(572\) −1.90820 + 1.60117i −0.0797857 + 0.0669481i
\(573\) 23.8025 8.66340i 0.994364 0.361919i
\(574\) −20.0996 + 7.31567i −0.838942 + 0.305350i
\(575\) 0.747444 0.627180i 0.0311706 0.0261552i
\(576\) 0.890081 + 5.04790i 0.0370867 + 0.210329i
\(577\) −5.92489 33.6017i −0.246656 1.39886i −0.816614 0.577184i \(-0.804152\pi\)
0.569958 0.821674i \(-0.306960\pi\)
\(578\) 17.5319 30.3662i 0.729231 1.26307i
\(579\) 19.0067 + 15.9485i 0.789891 + 0.662798i
\(580\) 3.65845 + 1.33157i 0.151909 + 0.0552902i
\(581\) 26.7042 + 46.2531i 1.10788 + 1.91890i
\(582\) 10.7173 18.5629i 0.444247 0.769459i
\(583\) 1.92988 1.61936i 0.0799276 0.0670672i
\(584\) 8.17032 + 14.1514i 0.338090 + 0.585589i
\(585\) −5.33945 + 30.2815i −0.220759 + 1.25199i
\(586\) 18.2839 0.755301
\(587\) 3.63042 20.5892i 0.149844 0.849806i −0.813506 0.581557i \(-0.802444\pi\)
0.963350 0.268249i \(-0.0864450\pi\)
\(588\) 25.6565 + 21.5284i 1.05806 + 0.887815i
\(589\) −25.5674 + 9.30578i −1.05349 + 0.383438i
\(590\) 5.39472 + 1.96352i 0.222097 + 0.0808367i
\(591\) −47.7900 −1.96582
\(592\) 3.67833 + 4.84458i 0.151178 + 0.199111i
\(593\) 22.1062 0.907792 0.453896 0.891055i \(-0.350034\pi\)
0.453896 + 0.891055i \(0.350034\pi\)
\(594\) 2.36449 + 0.860603i 0.0970161 + 0.0353110i
\(595\) −29.3593 + 10.6859i −1.20362 + 0.438080i
\(596\) 1.83504 + 1.53978i 0.0751662 + 0.0630720i
\(597\) −0.614881 + 3.48716i −0.0251654 + 0.142720i
\(598\) 5.85318 0.239354
\(599\) 6.37428 36.1503i 0.260446 1.47706i −0.521251 0.853403i \(-0.674534\pi\)
0.781697 0.623659i \(-0.214354\pi\)
\(600\) 1.42529 + 2.46867i 0.0581871 + 0.100783i
\(601\) 23.9202 20.0714i 0.975726 0.818731i −0.00771340 0.999970i \(-0.502455\pi\)
0.983439 + 0.181239i \(0.0580108\pi\)
\(602\) −1.49969 + 2.59753i −0.0611226 + 0.105867i
\(603\) 28.2452 + 48.9222i 1.15023 + 1.99226i
\(604\) −15.3264 5.57835i −0.623622 0.226980i
\(605\) −8.29440 6.95983i −0.337215 0.282957i
\(606\) 3.86447 6.69345i 0.156983 0.271903i
\(607\) 4.03076 + 22.8596i 0.163603 + 0.927841i 0.950493 + 0.310747i \(0.100579\pi\)
−0.786889 + 0.617094i \(0.788310\pi\)
\(608\) −1.03610 5.87600i −0.0420193 0.238303i
\(609\) 36.8120 30.8889i 1.49170 1.25168i
\(610\) −9.34981 + 3.40305i −0.378563 + 0.137786i
\(611\) 6.51526 2.37136i 0.263579 0.0959350i
\(612\) −28.3323 + 23.7736i −1.14526 + 0.960991i
\(613\) −2.11466 11.9928i −0.0854103 0.484386i −0.997267 0.0738778i \(-0.976463\pi\)
0.911857 0.410508i \(-0.134649\pi\)
\(614\) −1.07694 6.10761i −0.0434617 0.246483i
\(615\) −7.04064 + 12.1947i −0.283906 + 0.491740i
\(616\) 1.37736 + 1.15574i 0.0554955 + 0.0465663i
\(617\) 3.39967 + 1.23738i 0.136866 + 0.0498150i 0.409545 0.912290i \(-0.365688\pi\)
−0.272679 + 0.962105i \(0.587910\pi\)
\(618\) −12.3984 21.4746i −0.498735 0.863835i
\(619\) 17.1879 29.7704i 0.690842 1.19657i −0.280721 0.959790i \(-0.590573\pi\)
0.971562 0.236784i \(-0.0760932\pi\)
\(620\) 3.49321 2.93115i 0.140291 0.117718i
\(621\) −2.95627 5.12041i −0.118631 0.205475i
\(622\) 3.98359 22.5921i 0.159728 0.905860i
\(623\) −45.7702 −1.83374
\(624\) −2.96941 + 16.8403i −0.118871 + 0.674153i
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 18.8723 6.86895i 0.754288 0.274539i
\(627\) −6.63667 2.41555i −0.265043 0.0964678i
\(628\) 16.2265 0.647508
\(629\) −17.0024 + 40.4633i −0.677930 + 1.61338i
\(630\) 22.1948 0.884263
\(631\) 12.6329 + 4.59798i 0.502906 + 0.183043i 0.581001 0.813903i \(-0.302661\pi\)
−0.0780946 + 0.996946i \(0.524884\pi\)
\(632\) 2.69624 0.981351i 0.107251 0.0390361i
\(633\) 33.7116 + 28.2874i 1.33992 + 1.12432i
\(634\) 3.62517 20.5593i 0.143974 0.816516i
\(635\) 6.30197 0.250086
\(636\) 3.00316 17.0317i 0.119083 0.675352i
\(637\) 35.2410 + 61.0393i 1.39630 + 2.41846i
\(638\) 1.23842 1.03915i 0.0490294 0.0411405i
\(639\) −11.5911 + 20.0764i −0.458536 + 0.794208i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 25.4108 + 9.24876i 1.00366 + 0.365304i 0.790997 0.611821i \(-0.209563\pi\)
0.212668 + 0.977125i \(0.431785\pi\)
\(642\) 31.4707 + 26.4071i 1.24205 + 1.04220i
\(643\) 8.05719 13.9555i 0.317744 0.550349i −0.662273 0.749263i \(-0.730408\pi\)
0.980017 + 0.198913i \(0.0637413\pi\)
\(644\) −0.733647 4.16072i −0.0289098 0.163955i
\(645\) 0.342879 + 1.94456i 0.0135008 + 0.0765670i
\(646\) 32.9801 27.6736i 1.29759 1.08880i
\(647\) 0.303500 0.110465i 0.0119318 0.00434283i −0.336047 0.941845i \(-0.609090\pi\)
0.347979 + 0.937502i \(0.386868\pi\)
\(648\) 1.78188 0.648550i 0.0699988 0.0254775i
\(649\) 1.82616 1.53233i 0.0716830 0.0601492i
\(650\) 1.04169 + 5.90770i 0.0408583 + 0.231719i
\(651\) −9.77385 55.4303i −0.383067 2.17248i
\(652\) −1.77914 + 3.08156i −0.0696764 + 0.120683i
\(653\) 6.22427 + 5.22278i 0.243574 + 0.204383i 0.756400 0.654110i \(-0.226957\pi\)
−0.512825 + 0.858493i \(0.671401\pi\)
\(654\) −24.2558 8.82841i −0.948479 0.345218i
\(655\) 9.82197 + 17.0122i 0.383776 + 0.664720i
\(656\) −2.46990 + 4.27800i −0.0964335 + 0.167028i
\(657\) 64.1627 53.8389i 2.50322 2.10045i
\(658\) −2.50231 4.33413i −0.0975502 0.168962i
\(659\) 5.51578 31.2816i 0.214864 1.21856i −0.666277 0.745704i \(-0.732113\pi\)
0.881142 0.472852i \(-0.156776\pi\)
\(660\) 1.18368 0.0460747
\(661\) −5.10127 + 28.9307i −0.198416 + 1.12527i 0.709053 + 0.705155i \(0.249123\pi\)
−0.907469 + 0.420119i \(0.861988\pi\)
\(662\) −23.2561 19.5142i −0.903875 0.758441i
\(663\) −115.945 + 42.2007i −4.50294 + 1.63894i
\(664\) 11.5905 + 4.21861i 0.449800 + 0.163714i
\(665\) −25.8358 −1.00187
\(666\) 21.1809 22.8799i 0.820744 0.886578i
\(667\) −3.79871 −0.147086
\(668\) −6.37647 2.32084i −0.246713 0.0897962i
\(669\) 15.5983 5.67730i 0.603064 0.219497i
\(670\) 8.44247 + 7.08407i 0.326161 + 0.273682i
\(671\) −0.717446 + 4.06884i −0.0276967 + 0.157076i
\(672\) 12.3431 0.476146
\(673\) 5.12970 29.0920i 0.197735 1.12141i −0.710734 0.703461i \(-0.751637\pi\)
0.908469 0.417952i \(-0.137252\pi\)
\(674\) 3.55400 + 6.15571i 0.136895 + 0.237109i
\(675\) 4.64198 3.89508i 0.178670 0.149922i
\(676\) −11.4930 + 19.9065i −0.442040 + 0.765635i
\(677\) 5.84387 + 10.1219i 0.224598 + 0.389015i 0.956199 0.292718i \(-0.0945597\pi\)
−0.731601 + 0.681733i \(0.761226\pi\)
\(678\) 21.4470 + 7.80606i 0.823666 + 0.299790i
\(679\) −24.9419 20.9288i −0.957184 0.803172i
\(680\) −3.60776 + 6.24883i −0.138351 + 0.239632i
\(681\) −6.69996 37.9973i −0.256743 1.45606i
\(682\) −0.328808 1.86477i −0.0125907 0.0714056i
\(683\) 12.2739 10.2990i 0.469647 0.394081i −0.377019 0.926206i \(-0.623051\pi\)
0.846666 + 0.532125i \(0.178606\pi\)
\(684\) −28.7393 + 10.4602i −1.09887 + 0.399957i
\(685\) −7.87843 + 2.86751i −0.301019 + 0.109562i
\(686\) 15.7534 13.2187i 0.601468 0.504692i
\(687\) 6.05817 + 34.3576i 0.231134 + 1.31082i
\(688\) 0.120284 + 0.682165i 0.00458579 + 0.0260073i
\(689\) 18.1975 31.5190i 0.693270 1.20078i
\(690\) −2.13065 1.78782i −0.0811123 0.0680613i
\(691\) 7.66236 + 2.78887i 0.291490 + 0.106094i 0.483626 0.875275i \(-0.339319\pi\)
−0.192136 + 0.981368i \(0.561542\pi\)
\(692\) −6.66138 11.5379i −0.253228 0.438603i
\(693\) 4.60812 7.98150i 0.175048 0.303192i
\(694\) −25.9674 + 21.7892i −0.985707 + 0.827107i
\(695\) −5.35072 9.26772i −0.202964 0.351545i
\(696\) 1.92714 10.9294i 0.0730481 0.414276i
\(697\) −35.6433 −1.35009
\(698\) −4.51198 + 25.5887i −0.170781 + 0.968547i
\(699\) −6.90125 5.79083i −0.261029 0.219029i
\(700\) 4.06891 1.48096i 0.153790 0.0559751i
\(701\) 8.32397 + 3.02968i 0.314392 + 0.114429i 0.494397 0.869236i \(-0.335389\pi\)
−0.180005 + 0.983666i \(0.557611\pi\)
\(702\) 36.3510 1.37198
\(703\) −24.6556 + 26.6333i −0.929904 + 1.00449i
\(704\) 0.415243 0.0156500
\(705\) −3.09597 1.12684i −0.116601 0.0424393i
\(706\) −24.0259 + 8.74473i −0.904228 + 0.329112i
\(707\) −8.99360 7.54653i −0.338239 0.283816i
\(708\) 2.84175 16.1163i 0.106799 0.605689i
\(709\) 22.3893 0.840849 0.420425 0.907327i \(-0.361881\pi\)
0.420425 + 0.907327i \(0.361881\pi\)
\(710\) −0.785353 + 4.45396i −0.0294738 + 0.167154i
\(711\) −7.35364 12.7369i −0.275783 0.477670i
\(712\) −8.09738 + 6.79451i −0.303462 + 0.254635i
\(713\) −2.22467 + 3.85324i −0.0833146 + 0.144305i
\(714\) 44.5310 + 77.1300i 1.66653 + 2.88652i
\(715\) 2.34075 + 0.851963i 0.0875390 + 0.0318616i
\(716\) 16.7676 + 14.0697i 0.626633 + 0.525808i
\(717\) 12.4834 21.6220i 0.466203 0.807487i
\(718\) 3.00296 + 17.0306i 0.112069 + 0.635577i
\(719\) −3.55936 20.1862i −0.132742 0.752817i −0.976406 0.215945i \(-0.930717\pi\)
0.843664 0.536872i \(-0.180394\pi\)
\(720\) 3.92657 3.29478i 0.146335 0.122789i
\(721\) −35.3949 + 12.8827i −1.31817 + 0.479776i
\(722\) 15.5997 5.67783i 0.580561 0.211307i
\(723\) −3.30748 + 2.77530i −0.123006 + 0.103215i
\(724\) 1.28492 + 7.28713i 0.0477536 + 0.270824i
\(725\) −0.676053 3.83409i −0.0251080 0.142395i
\(726\) −15.4324 + 26.7297i −0.572750 + 0.992032i
\(727\) 25.9100 + 21.7411i 0.960950 + 0.806333i 0.981107 0.193464i \(-0.0619723\pi\)
−0.0201575 + 0.999797i \(0.506417\pi\)
\(728\) 24.4087 + 8.88405i 0.904648 + 0.329265i
\(729\) 21.0505 + 36.4605i 0.779648 + 1.35039i
\(730\) 8.17032 14.1514i 0.302397 0.523767i
\(731\) −3.82877 + 3.21272i −0.141612 + 0.118827i
\(732\) 14.1814 + 24.5629i 0.524160 + 0.907872i
\(733\) −5.85562 + 33.2089i −0.216282 + 1.22660i 0.662386 + 0.749163i \(0.269544\pi\)
−0.878668 + 0.477434i \(0.841567\pi\)
\(734\) 19.2925 0.712099
\(735\) 5.81586 32.9834i 0.214521 1.21661i
\(736\) −0.747444 0.627180i −0.0275512 0.0231182i
\(737\) 4.30035 1.56520i 0.158405 0.0576548i
\(738\) 23.7933 + 8.66006i 0.875844 + 0.318781i
\(739\) −36.6499 −1.34819 −0.674093 0.738646i \(-0.735465\pi\)
−0.674093 + 0.738646i \(0.735465\pi\)
\(740\) 2.35636 5.60781i 0.0866216 0.206147i
\(741\) −102.030 −3.74818
\(742\) −24.6861 8.98502i −0.906257 0.329851i
\(743\) 11.0083 4.00670i 0.403856 0.146992i −0.132102 0.991236i \(-0.542173\pi\)
0.535958 + 0.844245i \(0.319950\pi\)
\(744\) −9.95766 8.35547i −0.365065 0.306326i
\(745\) 0.415970 2.35908i 0.0152400 0.0864302i
\(746\) −9.45963 −0.346342
\(747\) 10.9786 62.2628i 0.401686 2.27808i
\(748\) 1.49810 + 2.59478i 0.0547758 + 0.0948745i
\(749\) 47.8043 40.1125i 1.74673 1.46568i
\(750\) 1.42529 2.46867i 0.0520441 0.0901431i
\(751\) −1.96003 3.39487i −0.0715225 0.123881i 0.828046 0.560660i \(-0.189452\pi\)
−0.899569 + 0.436779i \(0.856119\pi\)
\(752\) −1.08609 0.395303i −0.0396055 0.0144152i
\(753\) −28.2766 23.7269i −1.03046 0.864655i
\(754\) 11.6774 20.2259i 0.425268 0.736585i
\(755\) 2.83220 + 16.0622i 0.103074 + 0.584564i
\(756\) −4.55630 25.8400i −0.165711 0.939793i
\(757\) −36.6972 + 30.7926i −1.33378 + 1.11918i −0.350607 + 0.936523i \(0.614025\pi\)
−0.983177 + 0.182655i \(0.941531\pi\)
\(758\) 1.00974 0.367516i 0.0366755 0.0133488i
\(759\) −1.08529 + 0.395012i −0.0393934 + 0.0143380i
\(760\) −4.57072 + 3.83529i −0.165797 + 0.139120i
\(761\) −2.97826 16.8906i −0.107962 0.612283i −0.989996 0.141097i \(-0.954937\pi\)
0.882034 0.471186i \(-0.156174\pi\)
\(762\) −3.11946 17.6913i −0.113006 0.640889i
\(763\) −19.6047 + 33.9564i −0.709738 + 1.22930i
\(764\) −6.80704 5.71179i −0.246270 0.206645i
\(765\) 34.7547 + 12.6497i 1.25656 + 0.457350i
\(766\) 3.49732 + 6.05754i 0.126363 + 0.218868i
\(767\) 17.2195 29.8250i 0.621759 1.07692i
\(768\) 2.18367 1.83231i 0.0787963 0.0661179i
\(769\) −3.79804 6.57839i −0.136961 0.237223i 0.789384 0.613900i \(-0.210400\pi\)
−0.926345 + 0.376677i \(0.877067\pi\)
\(770\) 0.312223 1.77070i 0.0112517 0.0638117i
\(771\) 53.9681 1.94361
\(772\) 1.51144 8.57180i 0.0543979 0.308506i
\(773\) 7.26311 + 6.09447i 0.261236 + 0.219203i 0.763993 0.645225i \(-0.223236\pi\)
−0.502757 + 0.864428i \(0.667681\pi\)
\(774\) 3.33644 1.21436i 0.119926 0.0436494i
\(775\) −4.28506 1.55963i −0.153924 0.0560237i
\(776\) −7.51941 −0.269931
\(777\) −45.4020 59.7971i −1.62879 2.14521i
\(778\) −12.3240 −0.441835
\(779\) −27.6966 10.0807i −0.992332 0.361179i
\(780\) 16.0689 5.84859i 0.575358 0.209413i
\(781\) 1.43864 + 1.20716i 0.0514784 + 0.0431955i
\(782\) 1.22254 6.93337i 0.0437179 0.247937i
\(783\) −23.5918 −0.843100
\(784\) 2.04024 11.5708i 0.0728658 0.413242i
\(785\) −8.11325 14.0526i −0.289574 0.501557i
\(786\) 42.8958 35.9939i 1.53004 1.28386i
\(787\) −9.53091 + 16.5080i −0.339740 + 0.588447i −0.984384 0.176036i \(-0.943672\pi\)
0.644644 + 0.764483i \(0.277006\pi\)
\(788\) 8.38252 + 14.5190i 0.298615 + 0.517216i
\(789\) −32.3123 11.7607i −1.15035 0.418692i
\(790\) −2.19800 1.84434i −0.0782012 0.0656186i
\(791\) 17.3345 30.0241i 0.616342 1.06754i
\(792\) −0.369600 2.09610i −0.0131332 0.0744818i
\(793\) 10.3646 + 58.7808i 0.368059 + 2.08737i
\(794\) 2.10121 1.76312i 0.0745691 0.0625709i
\(795\) −16.2515 + 5.91506i −0.576381 + 0.209786i
\(796\) 1.16728 0.424855i 0.0413731 0.0150586i
\(797\) −23.6632 + 19.8558i −0.838192 + 0.703327i −0.957156 0.289572i \(-0.906487\pi\)
0.118964 + 0.992899i \(0.462043\pi\)
\(798\) 12.7887 + 72.5281i 0.452714 + 2.56747i
\(799\) −1.44816 8.21293i −0.0512323 0.290553i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 41.5053 + 34.8271i 1.46652 + 1.23056i
\(802\) 34.8410 + 12.6811i 1.23028 + 0.447784i
\(803\) −3.39266 5.87627i −0.119725 0.207369i
\(804\) 15.7079 27.2069i 0.553975 0.959512i
\(805\) −3.23647 + 2.71572i −0.114070 + 0.0957165i
\(806\) −13.6775 23.6902i −0.481771 0.834451i
\(807\) 11.4529 64.9528i 0.403162 2.28645i
\(808\) −2.71136 −0.0953853
\(809\) −4.13278 + 23.4381i −0.145301 + 0.824041i 0.821824 + 0.569741i \(0.192956\pi\)
−0.967125 + 0.254301i \(0.918155\pi\)
\(810\) −1.45260 1.21888i −0.0510392 0.0428269i
\(811\) −4.14482 + 1.50859i −0.145544 + 0.0529737i −0.413765 0.910384i \(-0.635787\pi\)
0.268221 + 0.963357i \(0.413564\pi\)
\(812\) −15.8412 5.76574i −0.555918 0.202338i
\(813\) −14.0678 −0.493380
\(814\) −1.52740 2.01167i −0.0535353 0.0705091i
\(815\) 3.55827 0.124641
\(816\) 19.3280 + 7.03481i 0.676614 + 0.246267i
\(817\) −3.88377 + 1.41358i −0.135876 + 0.0494548i
\(818\) −14.2888 11.9897i −0.499596 0.419211i
\(819\) 23.1201 131.120i 0.807881 4.58172i
\(820\) 4.93981 0.172505
\(821\) −7.64972 + 43.3837i −0.266977 + 1.51410i 0.496368 + 0.868112i \(0.334667\pi\)
−0.763345 + 0.645991i \(0.776445\pi\)
\(822\) 11.9497 + 20.6974i 0.416793 + 0.721906i
\(823\) 14.8299 12.4438i 0.516938 0.433763i −0.346624 0.938004i \(-0.612672\pi\)
0.863563 + 0.504241i \(0.168228\pi\)
\(824\) −4.34943 + 7.53343i −0.151519 + 0.262439i
\(825\) −0.591840 1.02510i −0.0206052 0.0356893i
\(826\) −23.3594 8.50211i −0.812776 0.295826i
\(827\) −12.4996 10.4884i −0.434653 0.364717i 0.399051 0.916929i \(-0.369340\pi\)
−0.833704 + 0.552212i \(0.813784\pi\)
\(828\) −2.50066 + 4.33127i −0.0869039 + 0.150522i
\(829\) 8.27040 + 46.9038i 0.287243 + 1.62903i 0.697163 + 0.716913i \(0.254446\pi\)
−0.409920 + 0.912122i \(0.634443\pi\)
\(830\) −2.14184 12.1470i −0.0743445 0.421629i
\(831\) −10.4199 + 8.74331i −0.361461 + 0.303302i
\(832\) 5.63706 2.05172i 0.195430 0.0711307i
\(833\) 79.6646 28.9955i 2.76021 1.00464i
\(834\) −23.3684 + 19.6084i −0.809180 + 0.678983i
\(835\) 1.17832 + 6.68261i 0.0407776 + 0.231261i
\(836\) 0.430232 + 2.43996i 0.0148799 + 0.0843879i
\(837\) −13.8163 + 23.9304i −0.477560 + 0.827157i
\(838\) 11.1219 + 9.33235i 0.384199 + 0.322381i
\(839\) 24.5574 + 8.93817i 0.847816 + 0.308580i 0.729150 0.684354i \(-0.239916\pi\)
0.118667 + 0.992934i \(0.462138\pi\)
\(840\) −6.17156 10.6894i −0.212939 0.368821i
\(841\) 6.92135 11.9881i 0.238667 0.413384i
\(842\) −25.8106 + 21.6577i −0.889493 + 0.746373i
\(843\) −17.6056 30.4938i −0.606369 1.05026i
\(844\) 2.68079 15.2035i 0.0922768 0.523327i
\(845\) 22.9861 0.790744
\(846\) −1.02875 + 5.83431i −0.0353690 + 0.200588i
\(847\) 35.9151 + 30.1364i 1.23406 + 1.03550i
\(848\) −5.70113 + 2.07504i −0.195778 + 0.0712572i
\(849\) 66.9189 + 24.3565i 2.29665 + 0.835913i
\(850\) 7.21553 0.247491
\(851\) −0.289078 + 5.92802i −0.00990947 + 0.203210i
\(852\) 12.8922 0.441680
\(853\) 4.36230 + 1.58775i 0.149362 + 0.0543634i 0.415619 0.909539i \(-0.363565\pi\)
−0.266257 + 0.963902i \(0.585787\pi\)
\(854\) 40.4851 14.7354i 1.38537 0.504234i
\(855\) 23.4285 + 19.6588i 0.801236 + 0.672317i
\(856\) 2.50259 14.1929i 0.0855369 0.485104i
\(857\) 45.8476 1.56613 0.783063 0.621942i \(-0.213656\pi\)
0.783063 + 0.621942i \(0.213656\pi\)
\(858\) 1.23302 6.99283i 0.0420947 0.238731i
\(859\) −5.22042 9.04204i −0.178119 0.308510i 0.763118 0.646260i \(-0.223668\pi\)
−0.941236 + 0.337749i \(0.890334\pi\)
\(860\) 0.530630 0.445251i 0.0180943 0.0151829i
\(861\) 30.4863 52.8038i 1.03897 1.79955i
\(862\) 4.15024 + 7.18843i 0.141358 + 0.244839i
\(863\) 21.0403 + 7.65803i 0.716219 + 0.260682i 0.674320 0.738439i \(-0.264437\pi\)
0.0418993 + 0.999122i \(0.486659\pi\)
\(864\) −4.64198 3.89508i −0.157923 0.132513i
\(865\) −6.66138 + 11.5379i −0.226494 + 0.392299i
\(866\) −0.402303 2.28158i −0.0136708 0.0775311i
\(867\) 17.3565 + 98.4335i 0.589457 + 3.34298i
\(868\) −15.1258 + 12.6920i −0.513402 + 0.430795i
\(869\) −1.11959 + 0.407499i −0.0379796 + 0.0138235i
\(870\) −10.4287 + 3.79573i −0.353565 + 0.128687i
\(871\) 50.6450 42.4962i 1.71604 1.43993i
\(872\) 1.57242 + 8.91763i 0.0532488 + 0.301989i
\(873\) 6.69289 + 37.9572i 0.226520 + 1.28466i
\(874\) 2.91089 5.04180i 0.0984622 0.170541i
\(875\) −3.31701 2.78330i −0.112135 0.0940927i
\(876\) −43.7711 15.9314i −1.47889 0.538271i
\(877\) 17.2030 + 29.7965i 0.580905 + 1.00616i 0.995372 + 0.0960931i \(0.0306346\pi\)
−0.414467 + 0.910064i \(0.636032\pi\)
\(878\) −6.22476 + 10.7816i −0.210076 + 0.363861i
\(879\) −39.9259 + 33.5018i −1.34667 + 1.12999i
\(880\) −0.207621 0.359611i −0.00699891 0.0121225i
\(881\) −2.82226 + 16.0058i −0.0950842 + 0.539249i 0.899637 + 0.436638i \(0.143831\pi\)
−0.994722 + 0.102611i \(0.967280\pi\)
\(882\) −60.2242 −2.02785
\(883\) 4.37290 24.7999i 0.147160 0.834585i −0.818448 0.574581i \(-0.805165\pi\)
0.965608 0.260004i \(-0.0837238\pi\)
\(884\) 33.1581 + 27.8229i 1.11523 + 0.935786i
\(885\) −15.3780 + 5.59715i −0.516927 + 0.188146i
\(886\) −5.30490 1.93082i −0.178221 0.0648673i
\(887\) 16.4963 0.553892 0.276946 0.960885i \(-0.410678\pi\)
0.276946 + 0.960885i \(0.410678\pi\)
\(888\) −16.9090 3.83909i −0.567430 0.128831i
\(889\) −27.2878 −0.915204
\(890\) 9.93290 + 3.61528i 0.332952 + 0.121185i
\(891\) −0.739911 + 0.269306i −0.0247880 + 0.00902208i
\(892\) −4.46079 3.74305i −0.149358 0.125327i
\(893\) 1.19751 6.79142i 0.0400731 0.227266i
\(894\) −6.82848 −0.228379
\(895\) 3.80090 21.5560i 0.127050 0.720537i
\(896\) −2.16502 3.74993i −0.0723283 0.125276i
\(897\) −12.7814 + 10.7249i −0.426758 + 0.358093i
\(898\) −13.8321 + 23.9578i −0.461582 + 0.799483i
\(899\) 8.87670 + 15.3749i 0.296055 + 0.512782i
\(900\) −4.81665 1.75312i −0.160555 0.0584373i
\(901\) −33.5349 28.1391i −1.11721 0.937450i
\(902\) 1.02561 1.77641i 0.0341490 0.0591479i
\(903\) −1.48468 8.42004i −0.0494070 0.280201i
\(904\) −1.39033 7.88495i −0.0462417 0.262250i
\(905\) 5.66838 4.75634i 0.188423 0.158106i
\(906\) 43.6890 15.9015i 1.45147 0.528292i
\(907\) −47.0393 + 17.1209i −1.56191 + 0.568490i −0.971174 0.238372i \(-0.923386\pi\)
−0.590740 + 0.806862i \(0.701164\pi\)
\(908\) −10.3687 + 8.70035i −0.344097 + 0.288731i
\(909\) 2.41333 + 13.6867i 0.0800451 + 0.453959i
\(910\) −4.51055 25.5806i −0.149523 0.847989i
\(911\) 16.7373 28.9898i 0.554530 0.960475i −0.443410 0.896319i \(-0.646231\pi\)
0.997940 0.0641556i \(-0.0204354\pi\)
\(912\) 13.0292 + 10.9328i 0.431439 + 0.362020i
\(913\) −4.81288 1.75175i −0.159283 0.0579744i
\(914\) 0.280544 + 0.485916i 0.00927957 + 0.0160727i
\(915\) 14.1814 24.5629i 0.468823 0.812025i
\(916\) 9.37547 7.86695i 0.309774 0.259931i
\(917\) −42.5296 73.6634i −1.40445 2.43258i
\(918\) 7.59255 43.0595i 0.250591 1.42117i
\(919\) −2.34412 −0.0773255 −0.0386628 0.999252i \(-0.512310\pi\)
−0.0386628 + 0.999252i \(0.512310\pi\)
\(920\) −0.169432 + 0.960896i −0.00558600 + 0.0316798i
\(921\) 13.5427 + 11.3637i 0.446248 + 0.374447i
\(922\) 2.39644 0.872233i 0.0789226 0.0287255i
\(923\) 25.4946 + 9.27927i 0.839164 + 0.305431i
\(924\) −5.12539 −0.168613
\(925\) −6.03469 + 0.763236i −0.198419 + 0.0250951i
\(926\) 21.5133 0.706972
\(927\) 41.8994 + 15.2501i 1.37616 + 0.500880i
\(928\) −3.65845 + 1.33157i −0.120094 + 0.0437108i
\(929\) −25.2900 21.2209i −0.829739 0.696234i 0.125492 0.992095i \(-0.459949\pi\)
−0.955231 + 0.295861i \(0.904393\pi\)
\(930\) −2.25722 + 12.8013i −0.0740171 + 0.419772i
\(931\) 70.1038 2.29756
\(932\) −0.548797 + 3.11238i −0.0179764 + 0.101949i
\(933\) 32.6969 + 56.6328i 1.07045 + 1.85407i
\(934\) −18.1609 + 15.2388i −0.594243 + 0.498629i
\(935\) 1.49810 2.59478i 0.0489930 0.0848584i
\(936\) −15.3743 26.6291i −0.502526 0.870401i
\(937\) 31.9256 + 11.6200i 1.04296 + 0.379607i 0.806003 0.591912i \(-0.201627\pi\)
0.236960 + 0.971519i \(0.423849\pi\)
\(938\) −36.5563 30.6744i −1.19360 1.00155i
\(939\) −28.6247 + 49.5795i −0.934132 + 1.61796i
\(940\) 0.200701 + 1.13823i 0.00654614 + 0.0371250i
\(941\) 3.98043 + 22.5741i 0.129758 + 0.735896i 0.978367 + 0.206875i \(0.0663294\pi\)
−0.848609 + 0.529020i \(0.822559\pi\)
\(942\) −35.4333 + 29.7320i −1.15448 + 0.968722i
\(943\) −4.52919 + 1.64849i −0.147491 + 0.0536822i
\(944\) −5.39472 + 1.96352i −0.175583 + 0.0639070i
\(945\) −20.1000 + 16.8659i −0.653853 + 0.548647i
\(946\) −0.0499470 0.283264i −0.00162392 0.00920970i
\(947\) −8.08973 45.8791i −0.262881 1.49087i −0.775002 0.631959i \(-0.782251\pi\)
0.512121 0.858913i \(-0.328860\pi\)
\(948\) −4.08955 + 7.08330i −0.132822 + 0.230055i
\(949\) −75.0914 63.0092i −2.43757 2.04536i
\(950\) 5.60681 + 2.04071i 0.181909 + 0.0662095i
\(951\) 29.7550 + 51.5372i 0.964872 + 1.67121i
\(952\) 15.6218 27.0577i 0.506305 0.876945i
\(953\) −10.9994 + 9.22959i −0.356305 + 0.298976i −0.803316 0.595553i \(-0.796933\pi\)
0.447011 + 0.894529i \(0.352489\pi\)
\(954\) 15.5491 + 26.9318i 0.503420 + 0.871949i
\(955\) −1.54303 + 8.75096i −0.0499313 + 0.283175i
\(956\) −8.75855 −0.283272
\(957\) −0.800231 + 4.53833i −0.0258678 + 0.146704i
\(958\) −19.9129 16.7089i −0.643357 0.539841i
\(959\) 34.1139 12.4165i 1.10160 0.400948i
\(960\) −2.67866 0.974954i −0.0864535 0.0314665i
\(961\) −10.2058 −0.329220
\(962\) −30.6747 19.7623i −0.988992 0.637161i
\(963\) −73.8720 −2.38049
\(964\) 1.42330 + 0.518039i 0.0458414 + 0.0166849i
\(965\) −8.17911 + 2.97695i −0.263295 + 0.0958315i
\(966\) 9.22579 + 7.74136i 0.296835 + 0.249074i
\(967\) −7.47716 + 42.4051i −0.240449 + 1.36365i 0.590379 + 0.807126i \(0.298978\pi\)
−0.830828 + 0.556529i \(0.812133\pi\)
\(968\) 10.8276 0.348011
\(969\) −21.3109 + 120.860i −0.684603 + 3.88258i
\(970\) 3.75971 + 6.51200i 0.120717 + 0.209088i
\(971\) −23.7825 + 19.9559i −0.763217 + 0.640415i −0.938962 0.344021i \(-0.888211\pi\)
0.175745 + 0.984436i \(0.443767\pi\)
\(972\) 6.38683 11.0623i 0.204858 0.354824i
\(973\) 23.1688 + 40.1296i 0.742759 + 1.28650i
\(974\) −1.34987 0.491314i −0.0432527 0.0157427i
\(975\) −13.0995 10.9918i −0.419519 0.352018i
\(976\) 4.97493 8.61683i 0.159244 0.275818i
\(977\) −3.20561 18.1799i −0.102557 0.581628i −0.992168 0.124910i \(-0.960136\pi\)
0.889611 0.456718i \(-0.150975\pi\)
\(978\) −1.76134 9.98903i −0.0563213 0.319414i
\(979\) 3.36238 2.82137i 0.107462 0.0901713i
\(980\) −11.0407 + 4.01849i −0.352683 + 0.128366i
\(981\) 43.6158 15.8748i 1.39254 0.506845i
\(982\) −18.3482 + 15.3960i −0.585515 + 0.491305i
\(983\) 0.463278 + 2.62738i 0.0147763 + 0.0838005i 0.991304 0.131591i \(-0.0420085\pi\)
−0.976528 + 0.215391i \(0.930897\pi\)
\(984\) −2.44519 13.8674i −0.0779498 0.442075i
\(985\) 8.38252 14.5190i 0.267089 0.462612i
\(986\) −21.5195 18.0570i −0.685322 0.575053i
\(987\) 13.4057 + 4.87927i 0.426708 + 0.155309i
\(988\) 17.8965 + 30.9976i 0.569363 + 0.986165i
\(989\) −0.337935 + 0.585320i −0.0107457 + 0.0186121i
\(990\) −1.63048 + 1.36813i −0.0518200 + 0.0434822i
\(991\) −8.50500 14.7311i −0.270170 0.467948i 0.698735 0.715380i \(-0.253747\pi\)
−0.968905 + 0.247432i \(0.920413\pi\)
\(992\) −0.791847 + 4.49079i −0.0251412 + 0.142583i
\(993\) 86.5398 2.74626
\(994\) 3.40062 19.2858i 0.107861 0.611710i
\(995\) −0.951574 0.798466i −0.0301669 0.0253131i
\(996\) −33.0397 + 12.0255i −1.04690 + 0.381041i
\(997\) 49.4991 + 18.0162i 1.56765 + 0.570579i 0.972474 0.233013i \(-0.0748585\pi\)
0.595180 + 0.803592i \(0.297081\pi\)
\(998\) 41.2383 1.30538
\(999\) −1.79531 + 36.8158i −0.0568011 + 1.16480i
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 370.2.o.c.201.1 yes 24
37.7 even 9 inner 370.2.o.c.81.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.o.c.81.1 24 37.7 even 9 inner
370.2.o.c.201.1 yes 24 1.1 even 1 trivial