Properties

Label 380.2.k.d.267.5
Level $380$
Weight $2$
Character 380.267
Analytic conductor $3.034$
Analytic rank $0$
Dimension $52$
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] = [380,2,Mod(267,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.267");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 267.5
Character \(\chi\) \(=\) 380.267
Dual form 380.2.k.d.343.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23831 + 0.683080i) q^{2} +(0.494605 + 0.494605i) q^{3} +(1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 - 0.274617i) q^{6} +(-0.327577 + 0.327577i) q^{7} +(-0.165443 + 2.82358i) q^{8} -2.51073i q^{9} +O(q^{10})\) \(q+(-1.23831 + 0.683080i) q^{2} +(0.494605 + 0.494605i) q^{3} +(1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 - 0.274617i) q^{6} +(-0.327577 + 0.327577i) q^{7} +(-0.165443 + 2.82358i) q^{8} -2.51073i q^{9} +(-0.385706 + 3.13867i) q^{10} -2.94834i q^{11} +(1.36438 - 0.309090i) q^{12} +(0.287718 - 0.287718i) q^{13} +(0.181879 - 0.629402i) q^{14} +(1.54434 - 0.247693i) q^{15} +(-1.72387 - 3.60947i) q^{16} +(-1.74168 - 1.74168i) q^{17} +(1.71503 + 3.10905i) q^{18} -1.00000 q^{19} +(-1.66634 - 4.15010i) q^{20} -0.324042 q^{21} +(2.01395 + 3.65095i) q^{22} +(-0.570036 - 0.570036i) q^{23} +(-1.47839 + 1.31473i) q^{24} +(-1.56365 - 4.74921i) q^{25} +(-0.159749 + 0.552818i) q^{26} +(2.72563 - 2.72563i) q^{27} +(0.204710 + 0.903630i) q^{28} -1.85155i q^{29} +(-1.74317 + 1.36163i) q^{30} +1.12279i q^{31} +(4.60023 + 3.29209i) q^{32} +(1.45826 - 1.45826i) q^{33} +(3.34643 + 0.967023i) q^{34} +(0.164047 + 1.02282i) q^{35} +(-4.24747 - 2.67846i) q^{36} +(4.08314 + 4.08314i) q^{37} +(1.23831 - 0.683080i) q^{38} +0.284614 q^{39} +(4.89829 + 4.00085i) q^{40} +10.4815 q^{41} +(0.401264 - 0.221347i) q^{42} +(7.09760 + 7.09760i) q^{43} +(-4.98778 - 3.14530i) q^{44} +(-4.54839 - 3.29105i) q^{45} +(1.09526 + 0.316498i) q^{46} +(2.57471 - 2.57471i) q^{47} +(0.932630 - 2.63789i) q^{48} +6.78539i q^{49} +(5.18037 + 4.81288i) q^{50} -1.72288i q^{51} +(-0.179802 - 0.793679i) q^{52} +(5.67543 - 5.67543i) q^{53} +(-1.51334 + 5.23700i) q^{54} +(-5.34116 - 3.86466i) q^{55} +(-0.870746 - 0.979137i) q^{56} +(-0.494605 - 0.494605i) q^{57} +(1.26476 + 2.29278i) q^{58} -14.1245 q^{59} +(1.22848 - 2.87684i) q^{60} +7.69452 q^{61} +(-0.766955 - 1.39036i) q^{62} +(0.822459 + 0.822459i) q^{63} +(-7.94526 - 0.934286i) q^{64} +(-0.144086 - 0.898364i) q^{65} +(-0.809664 + 2.80189i) q^{66} +(-9.51194 + 9.51194i) q^{67} +(-4.80446 + 1.08841i) q^{68} -0.563885i q^{69} +(-0.901807 - 1.15450i) q^{70} -9.19745i q^{71} +(7.08926 + 0.415384i) q^{72} +(-4.82935 + 4.82935i) q^{73} +(-7.84529 - 2.26706i) q^{74} +(1.57559 - 3.12237i) q^{75} +(-1.06680 + 1.69172i) q^{76} +(0.965809 + 0.965809i) q^{77} +(-0.352439 + 0.194414i) q^{78} -0.164126 q^{79} +(-8.79848 - 1.60834i) q^{80} -4.83597 q^{81} +(-12.9793 + 7.15972i) q^{82} +(-1.98305 - 1.98305i) q^{83} +(-0.345689 + 0.548191i) q^{84} +(-5.43817 + 0.872213i) q^{85} +(-13.6372 - 3.94077i) q^{86} +(0.915785 - 0.915785i) q^{87} +(8.32489 + 0.487783i) q^{88} +2.27564i q^{89} +(7.88035 + 0.968404i) q^{90} +0.188500i q^{91} +(-1.57246 + 0.356228i) q^{92} +(-0.555337 + 0.555337i) q^{93} +(-1.42954 + 4.94700i) q^{94} +(-1.31079 + 1.81158i) q^{95} +(0.647013 + 3.90358i) q^{96} +(-4.13745 - 4.13745i) q^{97} +(-4.63496 - 8.40238i) q^{98} -7.40249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23831 + 0.683080i −0.875614 + 0.483011i
\(3\) 0.494605 + 0.494605i 0.285560 + 0.285560i 0.835322 0.549762i \(-0.185281\pi\)
−0.549762 + 0.835322i \(0.685281\pi\)
\(4\) 1.06680 1.69172i 0.533401 0.845862i
\(5\) 1.31079 1.81158i 0.586204 0.810164i
\(6\) −0.950327 0.274617i −0.387969 0.112112i
\(7\) −0.327577 + 0.327577i −0.123813 + 0.123813i −0.766298 0.642485i \(-0.777903\pi\)
0.642485 + 0.766298i \(0.277903\pi\)
\(8\) −0.165443 + 2.82358i −0.0584930 + 0.998288i
\(9\) 2.51073i 0.836911i
\(10\) −0.385706 + 3.13867i −0.121971 + 0.992534i
\(11\) 2.94834i 0.888958i −0.895789 0.444479i \(-0.853389\pi\)
0.895789 0.444479i \(-0.146611\pi\)
\(12\) 1.36438 0.309090i 0.393863 0.0892265i
\(13\) 0.287718 0.287718i 0.0797987 0.0797987i −0.666081 0.745880i \(-0.732029\pi\)
0.745880 + 0.666081i \(0.232029\pi\)
\(14\) 0.181879 0.629402i 0.0486092 0.168215i
\(15\) 1.54434 0.247693i 0.398747 0.0639539i
\(16\) −1.72387 3.60947i −0.430966 0.902368i
\(17\) −1.74168 1.74168i −0.422419 0.422419i 0.463617 0.886036i \(-0.346551\pi\)
−0.886036 + 0.463617i \(0.846551\pi\)
\(18\) 1.71503 + 3.10905i 0.404237 + 0.732811i
\(19\) −1.00000 −0.229416
\(20\) −1.66634 4.15010i −0.372605 0.927990i
\(21\) −0.324042 −0.0707118
\(22\) 2.01395 + 3.65095i 0.429376 + 0.778384i
\(23\) −0.570036 0.570036i −0.118861 0.118861i 0.645175 0.764035i \(-0.276785\pi\)
−0.764035 + 0.645175i \(0.776785\pi\)
\(24\) −1.47839 + 1.31473i −0.301774 + 0.268368i
\(25\) −1.56365 4.74921i −0.312730 0.949842i
\(26\) −0.159749 + 0.552818i −0.0313293 + 0.108417i
\(27\) 2.72563 2.72563i 0.524549 0.524549i
\(28\) 0.204710 + 0.903630i 0.0386866 + 0.170770i
\(29\) 1.85155i 0.343824i −0.985112 0.171912i \(-0.945006\pi\)
0.985112 0.171912i \(-0.0549945\pi\)
\(30\) −1.74317 + 1.36163i −0.318258 + 0.248598i
\(31\) 1.12279i 0.201659i 0.994904 + 0.100829i \(0.0321496\pi\)
−0.994904 + 0.100829i \(0.967850\pi\)
\(32\) 4.60023 + 3.29209i 0.813214 + 0.581965i
\(33\) 1.45826 1.45826i 0.253851 0.253851i
\(34\) 3.34643 + 0.967023i 0.573909 + 0.165843i
\(35\) 0.164047 + 1.02282i 0.0277290 + 0.172888i
\(36\) −4.24747 2.67846i −0.707911 0.446409i
\(37\) 4.08314 + 4.08314i 0.671264 + 0.671264i 0.958007 0.286743i \(-0.0925727\pi\)
−0.286743 + 0.958007i \(0.592573\pi\)
\(38\) 1.23831 0.683080i 0.200880 0.110810i
\(39\) 0.284614 0.0455747
\(40\) 4.89829 + 4.00085i 0.774488 + 0.632589i
\(41\) 10.4815 1.63694 0.818470 0.574550i \(-0.194823\pi\)
0.818470 + 0.574550i \(0.194823\pi\)
\(42\) 0.401264 0.221347i 0.0619163 0.0341546i
\(43\) 7.09760 + 7.09760i 1.08237 + 1.08237i 0.996288 + 0.0860866i \(0.0274362\pi\)
0.0860866 + 0.996288i \(0.472564\pi\)
\(44\) −4.98778 3.14530i −0.751936 0.474171i
\(45\) −4.54839 3.29105i −0.678035 0.490600i
\(46\) 1.09526 + 0.316498i 0.161487 + 0.0466651i
\(47\) 2.57471 2.57471i 0.375559 0.375559i −0.493938 0.869497i \(-0.664443\pi\)
0.869497 + 0.493938i \(0.164443\pi\)
\(48\) 0.932630 2.63789i 0.134613 0.380747i
\(49\) 6.78539i 0.969341i
\(50\) 5.18037 + 4.81288i 0.732615 + 0.680643i
\(51\) 1.72288i 0.241252i
\(52\) −0.179802 0.793679i −0.0249340 0.110063i
\(53\) 5.67543 5.67543i 0.779580 0.779580i −0.200180 0.979759i \(-0.564153\pi\)
0.979759 + 0.200180i \(0.0641525\pi\)
\(54\) −1.51334 + 5.23700i −0.205940 + 0.712665i
\(55\) −5.34116 3.86466i −0.720201 0.521111i
\(56\) −0.870746 0.979137i −0.116358 0.130843i
\(57\) −0.494605 0.494605i −0.0655120 0.0655120i
\(58\) 1.26476 + 2.29278i 0.166071 + 0.301057i
\(59\) −14.1245 −1.83885 −0.919425 0.393265i \(-0.871345\pi\)
−0.919425 + 0.393265i \(0.871345\pi\)
\(60\) 1.22848 2.87684i 0.158596 0.371398i
\(61\) 7.69452 0.985182 0.492591 0.870261i \(-0.336050\pi\)
0.492591 + 0.870261i \(0.336050\pi\)
\(62\) −0.766955 1.39036i −0.0974034 0.176575i
\(63\) 0.822459 + 0.822459i 0.103620 + 0.103620i
\(64\) −7.94526 0.934286i −0.993157 0.116786i
\(65\) −0.144086 0.898364i −0.0178717 0.111428i
\(66\) −0.809664 + 2.80189i −0.0996628 + 0.344888i
\(67\) −9.51194 + 9.51194i −1.16207 + 1.16207i −0.178047 + 0.984022i \(0.556978\pi\)
−0.984022 + 0.178047i \(0.943022\pi\)
\(68\) −4.80446 + 1.08841i −0.582627 + 0.131990i
\(69\) 0.563885i 0.0678837i
\(70\) −0.901807 1.15450i −0.107787 0.137990i
\(71\) 9.19745i 1.09154i −0.837936 0.545768i \(-0.816238\pi\)
0.837936 0.545768i \(-0.183762\pi\)
\(72\) 7.08926 + 0.415384i 0.835478 + 0.0489535i
\(73\) −4.82935 + 4.82935i −0.565233 + 0.565233i −0.930789 0.365556i \(-0.880879\pi\)
0.365556 + 0.930789i \(0.380879\pi\)
\(74\) −7.84529 2.26706i −0.911996 0.263541i
\(75\) 1.57559 3.12237i 0.181934 0.360540i
\(76\) −1.06680 + 1.69172i −0.122371 + 0.194054i
\(77\) 0.965809 + 0.965809i 0.110064 + 0.110064i
\(78\) −0.352439 + 0.194414i −0.0399058 + 0.0220131i
\(79\) −0.164126 −0.0184656 −0.00923281 0.999957i \(-0.502939\pi\)
−0.00923281 + 0.999957i \(0.502939\pi\)
\(80\) −8.79848 1.60834i −0.983700 0.179818i
\(81\) −4.83597 −0.537331
\(82\) −12.9793 + 7.15972i −1.43333 + 0.790659i
\(83\) −1.98305 1.98305i −0.217667 0.217667i 0.589847 0.807515i \(-0.299188\pi\)
−0.807515 + 0.589847i \(0.799188\pi\)
\(84\) −0.345689 + 0.548191i −0.0377178 + 0.0598125i
\(85\) −5.43817 + 0.872213i −0.589852 + 0.0946048i
\(86\) −13.6372 3.94077i −1.47054 0.424944i
\(87\) 0.915785 0.915785i 0.0981825 0.0981825i
\(88\) 8.32489 + 0.487783i 0.887436 + 0.0519979i
\(89\) 2.27564i 0.241218i 0.992700 + 0.120609i \(0.0384847\pi\)
−0.992700 + 0.120609i \(0.961515\pi\)
\(90\) 7.88035 + 0.968404i 0.830662 + 0.102079i
\(91\) 0.188500i 0.0197602i
\(92\) −1.57246 + 0.356228i −0.163940 + 0.0371393i
\(93\) −0.555337 + 0.555337i −0.0575857 + 0.0575857i
\(94\) −1.42954 + 4.94700i −0.147446 + 0.510244i
\(95\) −1.31079 + 1.81158i −0.134484 + 0.185864i
\(96\) 0.647013 + 3.90358i 0.0660355 + 0.398407i
\(97\) −4.13745 4.13745i −0.420095 0.420095i 0.465141 0.885236i \(-0.346003\pi\)
−0.885236 + 0.465141i \(0.846003\pi\)
\(98\) −4.63496 8.40238i −0.468202 0.848769i
\(99\) −7.40249 −0.743978
\(100\) −9.70246 2.42120i −0.970246 0.242120i
\(101\) 4.60617 0.458331 0.229165 0.973387i \(-0.426400\pi\)
0.229165 + 0.973387i \(0.426400\pi\)
\(102\) 1.17687 + 2.13346i 0.116527 + 0.211244i
\(103\) 10.8229 + 10.8229i 1.06641 + 1.06641i 0.997632 + 0.0687770i \(0.0219097\pi\)
0.0687770 + 0.997632i \(0.478090\pi\)
\(104\) 0.764796 + 0.859998i 0.0749944 + 0.0843298i
\(105\) −0.424752 + 0.587029i −0.0414516 + 0.0572882i
\(106\) −3.15114 + 10.9047i −0.306066 + 1.05916i
\(107\) −5.10887 + 5.10887i −0.493893 + 0.493893i −0.909530 0.415637i \(-0.863559\pi\)
0.415637 + 0.909530i \(0.363559\pi\)
\(108\) −1.70331 7.51874i −0.163901 0.723491i
\(109\) 5.24030i 0.501930i 0.967996 + 0.250965i \(0.0807479\pi\)
−0.967996 + 0.250965i \(0.919252\pi\)
\(110\) 9.25386 + 1.13719i 0.882321 + 0.108427i
\(111\) 4.03908i 0.383372i
\(112\) 1.74708 + 0.617681i 0.165083 + 0.0583654i
\(113\) −9.13170 + 9.13170i −0.859038 + 0.859038i −0.991225 0.132186i \(-0.957800\pi\)
0.132186 + 0.991225i \(0.457800\pi\)
\(114\) 0.950327 + 0.274617i 0.0890062 + 0.0257202i
\(115\) −1.77986 + 0.285468i −0.165973 + 0.0266200i
\(116\) −3.13231 1.97524i −0.290828 0.183396i
\(117\) −0.722384 0.722384i −0.0667844 0.0667844i
\(118\) 17.4904 9.64815i 1.61012 0.888185i
\(119\) 1.14107 0.104601
\(120\) 0.443880 + 4.40155i 0.0405205 + 0.401805i
\(121\) 2.30729 0.209754
\(122\) −9.52816 + 5.25597i −0.862639 + 0.475853i
\(123\) 5.18421 + 5.18421i 0.467445 + 0.467445i
\(124\) 1.89945 + 1.19779i 0.170576 + 0.107565i
\(125\) −10.6532 3.39255i −0.952851 0.303439i
\(126\) −1.58026 0.456650i −0.140781 0.0406816i
\(127\) 0.359207 0.359207i 0.0318744 0.0318744i −0.690990 0.722864i \(-0.742825\pi\)
0.722864 + 0.690990i \(0.242825\pi\)
\(128\) 10.4769 4.27032i 0.926031 0.377446i
\(129\) 7.02101i 0.618166i
\(130\) 0.792078 + 1.01403i 0.0694698 + 0.0889360i
\(131\) 7.07602i 0.618235i −0.951024 0.309117i \(-0.899966\pi\)
0.951024 0.309117i \(-0.100034\pi\)
\(132\) −0.911301 4.02266i −0.0793186 0.350127i
\(133\) 0.327577 0.327577i 0.0284045 0.0284045i
\(134\) 5.28127 18.2761i 0.456232 1.57882i
\(135\) −1.36497 8.51044i −0.117478 0.732462i
\(136\) 5.20592 4.62962i 0.446404 0.396987i
\(137\) 4.32753 + 4.32753i 0.369726 + 0.369726i 0.867377 0.497651i \(-0.165804\pi\)
−0.497651 + 0.867377i \(0.665804\pi\)
\(138\) 0.385178 + 0.698261i 0.0327886 + 0.0594400i
\(139\) 11.4346 0.969873 0.484937 0.874549i \(-0.338843\pi\)
0.484937 + 0.874549i \(0.338843\pi\)
\(140\) 1.90533 + 0.813622i 0.161030 + 0.0687636i
\(141\) 2.54692 0.214490
\(142\) 6.28260 + 11.3893i 0.527224 + 0.955765i
\(143\) −0.848292 0.848292i −0.0709377 0.0709377i
\(144\) −9.06242 + 4.32817i −0.755201 + 0.360680i
\(145\) −3.35423 2.42700i −0.278554 0.201551i
\(146\) 2.68138 9.27905i 0.221912 0.767939i
\(147\) −3.35608 + 3.35608i −0.276805 + 0.276805i
\(148\) 11.2635 2.55165i 0.925850 0.209744i
\(149\) 13.1136i 1.07431i 0.843484 + 0.537155i \(0.180501\pi\)
−0.843484 + 0.537155i \(0.819499\pi\)
\(150\) 0.181764 + 4.94271i 0.0148409 + 0.403570i
\(151\) 2.25997i 0.183914i 0.995763 + 0.0919569i \(0.0293122\pi\)
−0.995763 + 0.0919569i \(0.970688\pi\)
\(152\) 0.165443 2.82358i 0.0134192 0.229023i
\(153\) −4.37289 + 4.37289i −0.353527 + 0.353527i
\(154\) −1.85569 0.536242i −0.149536 0.0432116i
\(155\) 2.03402 + 1.47174i 0.163377 + 0.118213i
\(156\) 0.303627 0.481488i 0.0243096 0.0385499i
\(157\) −11.4604 11.4604i −0.914642 0.914642i 0.0819909 0.996633i \(-0.473872\pi\)
−0.996633 + 0.0819909i \(0.973872\pi\)
\(158\) 0.203238 0.112111i 0.0161688 0.00891909i
\(159\) 5.61418 0.445234
\(160\) 11.9938 4.01845i 0.948196 0.317686i
\(161\) 0.373461 0.0294329
\(162\) 5.98842 3.30336i 0.470494 0.259536i
\(163\) −10.4983 10.4983i −0.822289 0.822289i 0.164147 0.986436i \(-0.447513\pi\)
−0.986436 + 0.164147i \(0.947513\pi\)
\(164\) 11.1817 17.7319i 0.873145 1.38463i
\(165\) −0.730282 4.55324i −0.0568524 0.354469i
\(166\) 3.81020 + 1.10104i 0.295729 + 0.0854570i
\(167\) 15.9796 15.9796i 1.23654 1.23654i 0.275136 0.961405i \(-0.411277\pi\)
0.961405 0.275136i \(-0.0887228\pi\)
\(168\) 0.0536106 0.914961i 0.00413615 0.0705908i
\(169\) 12.8344i 0.987264i
\(170\) 6.13832 4.79477i 0.470788 0.367742i
\(171\) 2.51073i 0.192001i
\(172\) 19.5789 4.43545i 1.49288 0.338200i
\(173\) −12.7302 + 12.7302i −0.967858 + 0.967858i −0.999499 0.0316413i \(-0.989927\pi\)
0.0316413 + 0.999499i \(0.489927\pi\)
\(174\) −0.508467 + 1.75958i −0.0385468 + 0.133393i
\(175\) 2.06795 + 1.04352i 0.156322 + 0.0788825i
\(176\) −10.6419 + 5.08254i −0.802167 + 0.383111i
\(177\) −6.98603 6.98603i −0.525102 0.525102i
\(178\) −1.55445 2.81794i −0.116511 0.211214i
\(179\) 3.57919 0.267522 0.133761 0.991014i \(-0.457295\pi\)
0.133761 + 0.991014i \(0.457295\pi\)
\(180\) −10.4198 + 4.18373i −0.776645 + 0.311837i
\(181\) −7.40488 −0.550400 −0.275200 0.961387i \(-0.588744\pi\)
−0.275200 + 0.961387i \(0.588744\pi\)
\(182\) −0.128761 0.233421i −0.00954437 0.0173023i
\(183\) 3.80574 + 3.80574i 0.281329 + 0.281329i
\(184\) 1.70385 1.51523i 0.125610 0.111705i
\(185\) 12.7491 2.04479i 0.937331 0.150336i
\(186\) 0.308337 1.06702i 0.0226084 0.0782374i
\(187\) −5.13506 + 5.13506i −0.375513 + 0.375513i
\(188\) −1.60899 7.10239i −0.117348 0.517995i
\(189\) 1.78571i 0.129891i
\(190\) 0.385706 3.13867i 0.0279820 0.227703i
\(191\) 4.12918i 0.298777i 0.988779 + 0.149388i \(0.0477304\pi\)
−0.988779 + 0.149388i \(0.952270\pi\)
\(192\) −3.46766 4.39186i −0.250257 0.316955i
\(193\) 5.54163 5.54163i 0.398895 0.398895i −0.478948 0.877843i \(-0.658982\pi\)
0.877843 + 0.478948i \(0.158982\pi\)
\(194\) 7.94965 + 2.29722i 0.570751 + 0.164931i
\(195\) 0.373069 0.515601i 0.0267161 0.0369229i
\(196\) 11.4790 + 7.23867i 0.819929 + 0.517048i
\(197\) 5.86112 + 5.86112i 0.417588 + 0.417588i 0.884371 0.466784i \(-0.154587\pi\)
−0.466784 + 0.884371i \(0.654587\pi\)
\(198\) 9.16655 5.05650i 0.651438 0.359350i
\(199\) 14.7472 1.04540 0.522701 0.852516i \(-0.324924\pi\)
0.522701 + 0.852516i \(0.324924\pi\)
\(200\) 13.6685 3.62937i 0.966508 0.256635i
\(201\) −9.40930 −0.663681
\(202\) −5.70385 + 3.14638i −0.401321 + 0.221379i
\(203\) 0.606525 + 0.606525i 0.0425697 + 0.0425697i
\(204\) −2.91464 1.83798i −0.204066 0.128684i
\(205\) 13.7391 18.9881i 0.959580 1.32619i
\(206\) −20.7949 6.00913i −1.44885 0.418676i
\(207\) −1.43121 + 1.43121i −0.0994757 + 0.0994757i
\(208\) −1.53450 0.542524i −0.106398 0.0376172i
\(209\) 2.94834i 0.203941i
\(210\) 0.124985 1.01706i 0.00862478 0.0701839i
\(211\) 3.44024i 0.236836i 0.992964 + 0.118418i \(0.0377822\pi\)
−0.992964 + 0.118418i \(0.962218\pi\)
\(212\) −3.54670 15.6558i −0.243588 1.07525i
\(213\) 4.54910 4.54910i 0.311699 0.311699i
\(214\) 2.83657 9.81611i 0.193904 0.671015i
\(215\) 22.1614 3.55440i 1.51139 0.242408i
\(216\) 7.24512 + 8.14700i 0.492968 + 0.554333i
\(217\) −0.367800 0.367800i −0.0249679 0.0249679i
\(218\) −3.57955 6.48910i −0.242438 0.439497i
\(219\) −4.77724 −0.322816
\(220\) −12.2359 + 4.91294i −0.824944 + 0.331230i
\(221\) −1.00223 −0.0674170
\(222\) −2.75902 5.00162i −0.185173 0.335686i
\(223\) 9.96172 + 9.96172i 0.667086 + 0.667086i 0.957040 0.289955i \(-0.0936402\pi\)
−0.289955 + 0.957040i \(0.593640\pi\)
\(224\) −2.58534 + 0.428517i −0.172741 + 0.0286315i
\(225\) −11.9240 + 3.92591i −0.794933 + 0.261727i
\(226\) 5.07015 17.5455i 0.337262 1.16711i
\(227\) −8.44789 + 8.44789i −0.560706 + 0.560706i −0.929508 0.368802i \(-0.879768\pi\)
0.368802 + 0.929508i \(0.379768\pi\)
\(228\) −1.36438 + 0.309090i −0.0903583 + 0.0204700i
\(229\) 8.64013i 0.570956i 0.958385 + 0.285478i \(0.0921524\pi\)
−0.958385 + 0.285478i \(0.907848\pi\)
\(230\) 2.00902 1.56929i 0.132471 0.103476i
\(231\) 0.955387i 0.0628599i
\(232\) 5.22801 + 0.306326i 0.343235 + 0.0201113i
\(233\) −4.54741 + 4.54741i −0.297911 + 0.297911i −0.840195 0.542284i \(-0.817560\pi\)
0.542284 + 0.840195i \(0.317560\pi\)
\(234\) 1.38798 + 0.401086i 0.0907350 + 0.0262198i
\(235\) −1.28938 8.03919i −0.0841101 0.524419i
\(236\) −15.0680 + 23.8947i −0.980845 + 1.55541i
\(237\) −0.0811775 0.0811775i −0.00527304 0.00527304i
\(238\) −1.41299 + 0.779441i −0.0915906 + 0.0505236i
\(239\) 23.0971 1.49403 0.747013 0.664810i \(-0.231487\pi\)
0.747013 + 0.664810i \(0.231487\pi\)
\(240\) −3.55627 5.14726i −0.229557 0.332254i
\(241\) 19.8422 1.27815 0.639075 0.769145i \(-0.279317\pi\)
0.639075 + 0.769145i \(0.279317\pi\)
\(242\) −2.85713 + 1.57607i −0.183663 + 0.101313i
\(243\) −10.5688 10.5688i −0.677989 0.677989i
\(244\) 8.20853 13.0170i 0.525497 0.833328i
\(245\) 12.2923 + 8.89423i 0.785325 + 0.568231i
\(246\) −9.96087 2.87841i −0.635082 0.183520i
\(247\) −0.287718 + 0.287718i −0.0183071 + 0.0183071i
\(248\) −3.17029 0.185758i −0.201314 0.0117956i
\(249\) 1.96165i 0.124314i
\(250\) 15.5093 3.07598i 0.980894 0.194542i
\(251\) 5.82734i 0.367819i −0.982943 0.183909i \(-0.941125\pi\)
0.982943 0.183909i \(-0.0588753\pi\)
\(252\) 2.26877 0.513973i 0.142919 0.0323772i
\(253\) −1.68066 + 1.68066i −0.105662 + 0.105662i
\(254\) −0.199441 + 0.690175i −0.0125140 + 0.0433054i
\(255\) −3.12114 2.25834i −0.195454 0.141423i
\(256\) −10.0566 + 12.4445i −0.628536 + 0.777781i
\(257\) 6.18949 + 6.18949i 0.386090 + 0.386090i 0.873290 0.487200i \(-0.161982\pi\)
−0.487200 + 0.873290i \(0.661982\pi\)
\(258\) −4.79592 8.69416i −0.298581 0.541275i
\(259\) −2.67509 −0.166222
\(260\) −1.67350 0.714623i −0.103786 0.0443190i
\(261\) −4.64874 −0.287750
\(262\) 4.83349 + 8.76227i 0.298614 + 0.541335i
\(263\) −8.45067 8.45067i −0.521091 0.521091i 0.396810 0.917901i \(-0.370117\pi\)
−0.917901 + 0.396810i \(0.870117\pi\)
\(264\) 3.87627 + 4.35879i 0.238568 + 0.268265i
\(265\) −2.84219 17.7208i −0.174594 1.08858i
\(266\) −0.181879 + 0.629402i −0.0111517 + 0.0385911i
\(267\) −1.12554 + 1.12554i −0.0688821 + 0.0688821i
\(268\) 5.94423 + 26.2390i 0.363101 + 1.60280i
\(269\) 1.50260i 0.0916154i −0.998950 0.0458077i \(-0.985414\pi\)
0.998950 0.0458077i \(-0.0145861\pi\)
\(270\) 7.50357 + 9.60615i 0.456652 + 0.584612i
\(271\) 29.6188i 1.79921i 0.436702 + 0.899606i \(0.356146\pi\)
−0.436702 + 0.899606i \(0.643854\pi\)
\(272\) −3.28412 + 9.28895i −0.199129 + 0.563226i
\(273\) −0.0932330 + 0.0932330i −0.00564272 + 0.00564272i
\(274\) −8.31485 2.40275i −0.502319 0.145156i
\(275\) −14.0023 + 4.61017i −0.844370 + 0.278004i
\(276\) −0.953937 0.601553i −0.0574203 0.0362093i
\(277\) −18.2366 18.2366i −1.09573 1.09573i −0.994904 0.100825i \(-0.967852\pi\)
−0.100825 0.994904i \(-0.532148\pi\)
\(278\) −14.1596 + 7.81078i −0.849235 + 0.468459i
\(279\) 2.81902 0.168771
\(280\) −2.91515 + 0.293982i −0.174214 + 0.0175688i
\(281\) 16.2476 0.969249 0.484625 0.874722i \(-0.338956\pi\)
0.484625 + 0.874722i \(0.338956\pi\)
\(282\) −3.15387 + 1.73975i −0.187810 + 0.103601i
\(283\) −6.63046 6.63046i −0.394140 0.394140i 0.482020 0.876160i \(-0.339903\pi\)
−0.876160 + 0.482020i \(0.839903\pi\)
\(284\) −15.5596 9.81186i −0.923290 0.582227i
\(285\) −1.54434 + 0.247693i −0.0914788 + 0.0146720i
\(286\) 1.62990 + 0.470993i 0.0963778 + 0.0278504i
\(287\) −3.43351 + 3.43351i −0.202674 + 0.202674i
\(288\) 8.26556 11.5500i 0.487053 0.680587i
\(289\) 10.9331i 0.643125i
\(290\) 5.81140 + 0.714153i 0.341257 + 0.0419365i
\(291\) 4.09281i 0.239925i
\(292\) 3.01797 + 13.3219i 0.176613 + 0.779605i
\(293\) −14.4511 + 14.4511i −0.844244 + 0.844244i −0.989408 0.145164i \(-0.953629\pi\)
0.145164 + 0.989408i \(0.453629\pi\)
\(294\) 1.86338 6.44833i 0.108675 0.376074i
\(295\) −18.5142 + 25.5876i −1.07794 + 1.48977i
\(296\) −12.2046 + 10.8536i −0.709379 + 0.630850i
\(297\) −8.03610 8.03610i −0.466302 0.466302i
\(298\) −8.95765 16.2387i −0.518903 0.940681i
\(299\) −0.328019 −0.0189699
\(300\) −3.60134 5.99642i −0.207924 0.346204i
\(301\) −4.65002 −0.268023
\(302\) −1.54374 2.79853i −0.0888323 0.161038i
\(303\) 2.27823 + 2.27823i 0.130881 + 0.130881i
\(304\) 1.72387 + 3.60947i 0.0988705 + 0.207017i
\(305\) 10.0859 13.9392i 0.577517 0.798158i
\(306\) 2.42794 8.40200i 0.138796 0.480310i
\(307\) −11.3650 + 11.3650i −0.648638 + 0.648638i −0.952664 0.304026i \(-0.901669\pi\)
0.304026 + 0.952664i \(0.401669\pi\)
\(308\) 2.66421 0.603556i 0.151807 0.0343908i
\(309\) 10.7061i 0.609048i
\(310\) −3.52406 0.433066i −0.200153 0.0245965i
\(311\) 31.6342i 1.79381i −0.442225 0.896904i \(-0.645811\pi\)
0.442225 0.896904i \(-0.354189\pi\)
\(312\) −0.0470874 + 0.803631i −0.00266580 + 0.0454966i
\(313\) −4.11199 + 4.11199i −0.232424 + 0.232424i −0.813704 0.581280i \(-0.802552\pi\)
0.581280 + 0.813704i \(0.302552\pi\)
\(314\) 22.0199 + 6.36312i 1.24266 + 0.359092i
\(315\) 2.56802 0.411878i 0.144692 0.0232067i
\(316\) −0.175090 + 0.277656i −0.00984958 + 0.0156194i
\(317\) 21.3697 + 21.3697i 1.20024 + 1.20024i 0.974093 + 0.226149i \(0.0726137\pi\)
0.226149 + 0.974093i \(0.427386\pi\)
\(318\) −6.95208 + 3.83494i −0.389853 + 0.215053i
\(319\) −5.45900 −0.305645
\(320\) −12.1071 + 13.1688i −0.676808 + 0.736159i
\(321\) −5.05374 −0.282072
\(322\) −0.462459 + 0.255104i −0.0257718 + 0.0142164i
\(323\) 1.74168 + 1.74168i 0.0969095 + 0.0969095i
\(324\) −5.15903 + 8.18114i −0.286613 + 0.454508i
\(325\) −1.81633 0.916545i −0.100752 0.0508407i
\(326\) 20.1713 + 5.82891i 1.11718 + 0.322834i
\(327\) −2.59188 + 2.59188i −0.143331 + 0.143331i
\(328\) −1.73410 + 29.5955i −0.0957496 + 1.63414i
\(329\) 1.68683i 0.0929979i
\(330\) 4.01454 + 5.13946i 0.220993 + 0.282918i
\(331\) 28.8144i 1.58378i −0.610661 0.791892i \(-0.709096\pi\)
0.610661 0.791892i \(-0.290904\pi\)
\(332\) −5.47028 + 1.23925i −0.300221 + 0.0680127i
\(333\) 10.2517 10.2517i 0.561788 0.561788i
\(334\) −8.87230 + 30.7030i −0.485471 + 1.68000i
\(335\) 4.76348 + 29.6998i 0.260256 + 1.62268i
\(336\) 0.558606 + 1.16962i 0.0304744 + 0.0638081i
\(337\) −13.4380 13.4380i −0.732016 0.732016i 0.239003 0.971019i \(-0.423179\pi\)
−0.971019 + 0.239003i \(0.923179\pi\)
\(338\) −8.76695 15.8930i −0.476859 0.864463i
\(339\) −9.03317 −0.490614
\(340\) −4.32590 + 10.1304i −0.234605 + 0.549396i
\(341\) 3.31036 0.179266
\(342\) −1.71503 3.10905i −0.0927383 0.168118i
\(343\) −4.51578 4.51578i −0.243829 0.243829i
\(344\) −21.2149 + 18.8664i −1.14383 + 1.01721i
\(345\) −1.02152 0.739135i −0.0549969 0.0397937i
\(346\) 7.06812 24.4596i 0.379985 1.31496i
\(347\) −19.6995 + 19.6995i −1.05752 + 1.05752i −0.0592835 + 0.998241i \(0.518882\pi\)
−0.998241 + 0.0592835i \(0.981118\pi\)
\(348\) −0.572295 2.52622i −0.0306782 0.135419i
\(349\) 7.57450i 0.405454i −0.979235 0.202727i \(-0.935020\pi\)
0.979235 0.202727i \(-0.0649804\pi\)
\(350\) −3.27356 + 0.120382i −0.174979 + 0.00643470i
\(351\) 1.56843i 0.0837166i
\(352\) 9.70620 13.5630i 0.517342 0.722913i
\(353\) −12.3157 + 12.3157i −0.655498 + 0.655498i −0.954311 0.298814i \(-0.903409\pi\)
0.298814 + 0.954311i \(0.403409\pi\)
\(354\) 13.4229 + 3.87882i 0.713417 + 0.206157i
\(355\) −16.6619 12.0559i −0.884323 0.639863i
\(356\) 3.84976 + 2.42766i 0.204037 + 0.128666i
\(357\) 0.564377 + 0.564377i 0.0298700 + 0.0298700i
\(358\) −4.43214 + 2.44488i −0.234246 + 0.129216i
\(359\) 23.4554 1.23793 0.618966 0.785418i \(-0.287552\pi\)
0.618966 + 0.785418i \(0.287552\pi\)
\(360\) 10.0451 12.2983i 0.529421 0.648177i
\(361\) 1.00000 0.0526316
\(362\) 9.16950 5.05813i 0.481938 0.265849i
\(363\) 1.14120 + 1.14120i 0.0598973 + 0.0598973i
\(364\) 0.318890 + 0.201092i 0.0167144 + 0.0105401i
\(365\) 2.41849 + 15.0790i 0.126589 + 0.789273i
\(366\) −7.31230 2.11305i −0.382220 0.110451i
\(367\) 23.3564 23.3564i 1.21920 1.21920i 0.251282 0.967914i \(-0.419148\pi\)
0.967914 0.251282i \(-0.0808523\pi\)
\(368\) −1.07486 + 3.04019i −0.0560311 + 0.158481i
\(369\) 26.3163i 1.36997i
\(370\) −14.3905 + 11.2407i −0.748127 + 0.584377i
\(371\) 3.71828i 0.193043i
\(372\) 0.347042 + 1.53191i 0.0179933 + 0.0794259i
\(373\) 6.12552 6.12552i 0.317168 0.317168i −0.530511 0.847678i \(-0.678000\pi\)
0.847678 + 0.530511i \(0.178000\pi\)
\(374\) 2.85111 9.86643i 0.147428 0.510181i
\(375\) −3.59115 6.94709i −0.185446 0.358746i
\(376\) 6.84393 + 7.69586i 0.352949 + 0.396884i
\(377\) −0.532725 0.532725i −0.0274367 0.0274367i
\(378\) −1.21978 2.21126i −0.0627389 0.113735i
\(379\) −22.9714 −1.17996 −0.589981 0.807417i \(-0.700865\pi\)
−0.589981 + 0.807417i \(0.700865\pi\)
\(380\) 1.66634 + 4.15010i 0.0854815 + 0.212896i
\(381\) 0.355331 0.0182041
\(382\) −2.82056 5.11318i −0.144312 0.261613i
\(383\) −18.5545 18.5545i −0.948090 0.948090i 0.0506273 0.998718i \(-0.483878\pi\)
−0.998718 + 0.0506273i \(0.983878\pi\)
\(384\) 7.29402 + 3.06978i 0.372221 + 0.156654i
\(385\) 3.01561 0.483666i 0.153690 0.0246499i
\(386\) −3.07685 + 10.6476i −0.156608 + 0.541949i
\(387\) 17.8202 17.8202i 0.905851 0.905851i
\(388\) −11.4133 + 2.58559i −0.579422 + 0.131263i
\(389\) 37.2211i 1.88718i −0.331112 0.943592i \(-0.607424\pi\)
0.331112 0.943592i \(-0.392576\pi\)
\(390\) −0.109777 + 0.893308i −0.00555878 + 0.0452344i
\(391\) 1.98564i 0.100418i
\(392\) −19.1591 1.12260i −0.967681 0.0566997i
\(393\) 3.49983 3.49983i 0.176543 0.176543i
\(394\) −11.2615 3.25424i −0.567345 0.163946i
\(395\) −0.215135 + 0.297327i −0.0108246 + 0.0149602i
\(396\) −7.89700 + 12.5230i −0.396839 + 0.629303i
\(397\) 8.21621 + 8.21621i 0.412360 + 0.412360i 0.882560 0.470200i \(-0.155818\pi\)
−0.470200 + 0.882560i \(0.655818\pi\)
\(398\) −18.2616 + 10.0735i −0.915369 + 0.504941i
\(399\) 0.324042 0.0162224
\(400\) −14.4466 + 13.8310i −0.722331 + 0.691548i
\(401\) 28.5885 1.42764 0.713821 0.700328i \(-0.246963\pi\)
0.713821 + 0.700328i \(0.246963\pi\)
\(402\) 11.6516 6.42731i 0.581129 0.320565i
\(403\) 0.323047 + 0.323047i 0.0160921 + 0.0160921i
\(404\) 4.91387 7.79237i 0.244474 0.387685i
\(405\) −6.33896 + 8.76076i −0.314985 + 0.435326i
\(406\) −1.16537 0.336758i −0.0578363 0.0167130i
\(407\) 12.0385 12.0385i 0.596725 0.596725i
\(408\) 4.86471 + 0.285040i 0.240839 + 0.0141116i
\(409\) 8.40060i 0.415383i 0.978194 + 0.207691i \(0.0665950\pi\)
−0.978194 + 0.207691i \(0.933405\pi\)
\(410\) −4.04278 + 32.8980i −0.199659 + 1.62472i
\(411\) 4.28083i 0.211158i
\(412\) 29.8552 6.76346i 1.47086 0.333212i
\(413\) 4.62686 4.62686i 0.227673 0.227673i
\(414\) 0.794642 2.74990i 0.0390545 0.135150i
\(415\) −6.19181 + 0.993087i −0.303944 + 0.0487487i
\(416\) 2.27077 0.376376i 0.111334 0.0184534i
\(417\) 5.65562 + 5.65562i 0.276957 + 0.276957i
\(418\) −2.01395 3.65095i −0.0985057 0.178574i
\(419\) −14.2962 −0.698416 −0.349208 0.937045i \(-0.613549\pi\)
−0.349208 + 0.937045i \(0.613549\pi\)
\(420\) 0.539965 + 1.34481i 0.0263476 + 0.0656199i
\(421\) 40.0754 1.95316 0.976579 0.215161i \(-0.0690275\pi\)
0.976579 + 0.215161i \(0.0690275\pi\)
\(422\) −2.34996 4.26007i −0.114394 0.207377i
\(423\) −6.46440 6.46440i −0.314310 0.314310i
\(424\) 15.0861 + 16.9640i 0.732645 + 0.823845i
\(425\) −5.54822 + 10.9950i −0.269128 + 0.533334i
\(426\) −2.52578 + 8.74058i −0.122374 + 0.423483i
\(427\) −2.52055 + 2.52055i −0.121978 + 0.121978i
\(428\) 3.19265 + 14.0930i 0.154322 + 0.681209i
\(429\) 0.839138i 0.0405140i
\(430\) −25.0146 + 19.5394i −1.20631 + 0.942275i
\(431\) 30.3005i 1.45952i 0.683702 + 0.729761i \(0.260369\pi\)
−0.683702 + 0.729761i \(0.739631\pi\)
\(432\) −14.5367 5.13947i −0.699399 0.247273i
\(433\) 4.16829 4.16829i 0.200315 0.200315i −0.599820 0.800135i \(-0.704761\pi\)
0.800135 + 0.599820i \(0.204761\pi\)
\(434\) 0.706686 + 0.204212i 0.0339220 + 0.00980249i
\(435\) −0.458615 2.85942i −0.0219889 0.137099i
\(436\) 8.86515 + 5.59037i 0.424564 + 0.267730i
\(437\) 0.570036 + 0.570036i 0.0272685 + 0.0272685i
\(438\) 5.91568 3.26324i 0.282662 0.155924i
\(439\) 19.3441 0.923241 0.461621 0.887077i \(-0.347268\pi\)
0.461621 + 0.887077i \(0.347268\pi\)
\(440\) 11.7959 14.4418i 0.562345 0.688487i
\(441\) 17.0363 0.811252
\(442\) 1.24106 0.684600i 0.0590313 0.0325631i
\(443\) −4.15922 4.15922i −0.197611 0.197611i 0.601364 0.798975i \(-0.294624\pi\)
−0.798975 + 0.601364i \(0.794624\pi\)
\(444\) 6.83301 + 4.30890i 0.324280 + 0.204491i
\(445\) 4.12251 + 2.98289i 0.195426 + 0.141403i
\(446\) −19.1403 5.53100i −0.906320 0.261900i
\(447\) −6.48606 + 6.48606i −0.306780 + 0.306780i
\(448\) 2.90874 2.29663i 0.137425 0.108506i
\(449\) 22.1626i 1.04592i 0.852358 + 0.522959i \(0.175172\pi\)
−0.852358 + 0.522959i \(0.824828\pi\)
\(450\) 12.0838 13.0065i 0.569638 0.613133i
\(451\) 30.9031i 1.45517i
\(452\) 5.70661 + 25.1901i 0.268416 + 1.18484i
\(453\) −1.11779 + 1.11779i −0.0525184 + 0.0525184i
\(454\) 4.69048 16.2317i 0.220135 0.761789i
\(455\) 0.341483 + 0.247084i 0.0160090 + 0.0115835i
\(456\) 1.47839 1.31473i 0.0692318 0.0615678i
\(457\) 10.8450 + 10.8450i 0.507307 + 0.507307i 0.913699 0.406392i \(-0.133213\pi\)
−0.406392 + 0.913699i \(0.633213\pi\)
\(458\) −5.90191 10.6991i −0.275778 0.499937i
\(459\) −9.49435 −0.443158
\(460\) −1.41583 + 3.31558i −0.0660134 + 0.154590i
\(461\) −6.29625 −0.293245 −0.146623 0.989192i \(-0.546840\pi\)
−0.146623 + 0.989192i \(0.546840\pi\)
\(462\) −0.652606 1.18306i −0.0303620 0.0550410i
\(463\) 5.60774 + 5.60774i 0.260614 + 0.260614i 0.825303 0.564690i \(-0.191004\pi\)
−0.564690 + 0.825303i \(0.691004\pi\)
\(464\) −6.68312 + 3.19182i −0.310256 + 0.148177i
\(465\) 0.278107 + 1.73397i 0.0128969 + 0.0804109i
\(466\) 2.52484 8.73733i 0.116961 0.404749i
\(467\) 23.6709 23.6709i 1.09536 1.09536i 0.100413 0.994946i \(-0.467983\pi\)
0.994946 0.100413i \(-0.0320165\pi\)
\(468\) −1.99272 + 0.451434i −0.0921133 + 0.0208675i
\(469\) 6.23179i 0.287757i
\(470\) 7.08806 + 9.07422i 0.326948 + 0.418563i
\(471\) 11.3368i 0.522371i
\(472\) 2.33680 39.8817i 0.107560 1.83570i
\(473\) 20.9261 20.9261i 0.962185 0.962185i
\(474\) 0.155973 + 0.0450718i 0.00716409 + 0.00207022i
\(475\) 1.56365 + 4.74921i 0.0717452 + 0.217909i
\(476\) 1.21729 1.93037i 0.0557945 0.0884785i
\(477\) −14.2495 14.2495i −0.652439 0.652439i
\(478\) −28.6012 + 15.7772i −1.30819 + 0.721631i
\(479\) 12.8003 0.584863 0.292431 0.956286i \(-0.405536\pi\)
0.292431 + 0.956286i \(0.405536\pi\)
\(480\) 7.91975 + 3.94466i 0.361485 + 0.180048i
\(481\) 2.34959 0.107132
\(482\) −24.5707 + 13.5538i −1.11917 + 0.617360i
\(483\) 0.184716 + 0.184716i 0.00840485 + 0.00840485i
\(484\) 2.46142 3.90330i 0.111883 0.177423i
\(485\) −12.9187 + 2.07199i −0.586607 + 0.0940843i
\(486\) 20.3067 + 5.86806i 0.921133 + 0.266181i
\(487\) 10.7519 10.7519i 0.487215 0.487215i −0.420211 0.907426i \(-0.638044\pi\)
0.907426 + 0.420211i \(0.138044\pi\)
\(488\) −1.27301 + 21.7261i −0.0576263 + 0.983495i
\(489\) 10.3850i 0.469626i
\(490\) −21.2971 2.61716i −0.962104 0.118231i
\(491\) 39.2711i 1.77228i 0.463417 + 0.886140i \(0.346623\pi\)
−0.463417 + 0.886140i \(0.653377\pi\)
\(492\) 14.3008 3.23973i 0.644729 0.146058i
\(493\) −3.22480 + 3.22480i −0.145238 + 0.145238i
\(494\) 0.159749 0.552818i 0.00718743 0.0248725i
\(495\) −9.70313 + 13.4102i −0.436123 + 0.602744i
\(496\) 4.05268 1.93554i 0.181971 0.0869082i
\(497\) 3.01287 + 3.01287i 0.135146 + 0.135146i
\(498\) 1.33996 + 2.42912i 0.0600452 + 0.108851i
\(499\) −35.8517 −1.60494 −0.802471 0.596692i \(-0.796482\pi\)
−0.802471 + 0.596692i \(0.796482\pi\)
\(500\) −17.1041 + 14.4031i −0.764919 + 0.644126i
\(501\) 15.8072 0.706214
\(502\) 3.98054 + 7.21603i 0.177660 + 0.322067i
\(503\) −8.36832 8.36832i −0.373125 0.373125i 0.495489 0.868614i \(-0.334989\pi\)
−0.868614 + 0.495489i \(0.834989\pi\)
\(504\) −2.45835 + 2.18621i −0.109504 + 0.0973816i
\(505\) 6.03773 8.34445i 0.268675 0.371323i
\(506\) 0.933144 3.22919i 0.0414833 0.143555i
\(507\) −6.34797 + 6.34797i −0.281923 + 0.281923i
\(508\) −0.224476 0.990881i −0.00995953 0.0439632i
\(509\) 8.31464i 0.368540i −0.982876 0.184270i \(-0.941008\pi\)
0.982876 0.184270i \(-0.0589921\pi\)
\(510\) 5.40756 + 0.664526i 0.239451 + 0.0294257i
\(511\) 3.16397i 0.139966i
\(512\) 3.95253 22.2795i 0.174679 0.984626i
\(513\) −2.72563 + 2.72563i −0.120340 + 0.120340i
\(514\) −11.8924 3.43656i −0.524551 0.151580i
\(515\) 33.7930 5.41997i 1.48910 0.238833i
\(516\) 11.8776 + 7.49003i 0.522883 + 0.329730i
\(517\) −7.59111 7.59111i −0.333856 0.333856i
\(518\) 3.31257 1.82730i 0.145546 0.0802869i
\(519\) −12.5928 −0.552763
\(520\) 2.56044 0.258211i 0.112283 0.0113233i
\(521\) −35.8196 −1.56928 −0.784642 0.619949i \(-0.787153\pi\)
−0.784642 + 0.619949i \(0.787153\pi\)
\(522\) 5.75657 3.17547i 0.251958 0.138986i
\(523\) 14.4962 + 14.4962i 0.633874 + 0.633874i 0.949038 0.315163i \(-0.102059\pi\)
−0.315163 + 0.949038i \(0.602059\pi\)
\(524\) −11.9707 7.54871i −0.522941 0.329767i
\(525\) 0.506689 + 1.53895i 0.0221137 + 0.0671651i
\(526\) 16.2370 + 4.69203i 0.707967 + 0.204582i
\(527\) 1.95554 1.95554i 0.0851845 0.0851845i
\(528\) −7.77741 2.74971i −0.338468 0.119666i
\(529\) 22.3501i 0.971744i
\(530\) 15.6242 + 20.0023i 0.678673 + 0.868845i
\(531\) 35.4628i 1.53895i
\(532\) −0.204710 0.903630i −0.00887532 0.0391773i
\(533\) 3.01573 3.01573i 0.130626 0.130626i
\(534\) 0.624930 2.16260i 0.0270434 0.0935850i
\(535\) 2.55847 + 15.9518i 0.110612 + 0.689656i
\(536\) −25.2841 28.4315i −1.09211 1.22805i
\(537\) 1.77029 + 1.77029i 0.0763935 + 0.0763935i
\(538\) 1.02640 + 1.86068i 0.0442512 + 0.0802198i
\(539\) 20.0056 0.861703
\(540\) −15.8535 6.76981i −0.682225 0.291326i
\(541\) −43.9873 −1.89116 −0.945580 0.325390i \(-0.894504\pi\)
−0.945580 + 0.325390i \(0.894504\pi\)
\(542\) −20.2320 36.6771i −0.869039 1.57542i
\(543\) −3.66249 3.66249i −0.157172 0.157172i
\(544\) −2.27836 13.7459i −0.0976839 0.589350i
\(545\) 9.49323 + 6.86895i 0.406645 + 0.294233i
\(546\) 0.0517653 0.179137i 0.00221535 0.00766634i
\(547\) 25.2995 25.2995i 1.08173 1.08173i 0.0853805 0.996348i \(-0.472789\pi\)
0.996348 0.0853805i \(-0.0272106\pi\)
\(548\) 11.9376 2.70437i 0.509949 0.115525i
\(549\) 19.3189i 0.824509i
\(550\) 14.1900 15.2735i 0.605063 0.651264i
\(551\) 1.85155i 0.0788787i
\(552\) 1.59218 + 0.0932909i 0.0677675 + 0.00397073i
\(553\) 0.0537639 0.0537639i 0.00228627 0.00228627i
\(554\) 35.0395 + 10.1254i 1.48869 + 0.430187i
\(555\) 7.31712 + 5.29439i 0.310594 + 0.224734i
\(556\) 12.1985 19.3443i 0.517331 0.820379i
\(557\) −11.2381 11.2381i −0.476172 0.476172i 0.427733 0.903905i \(-0.359312\pi\)
−0.903905 + 0.427733i \(0.859312\pi\)
\(558\) −3.49081 + 1.92562i −0.147778 + 0.0815180i
\(559\) 4.08422 0.172744
\(560\) 3.40904 2.35532i 0.144058 0.0995306i
\(561\) −5.07965 −0.214463
\(562\) −20.1195 + 11.0984i −0.848689 + 0.468158i
\(563\) −0.343770 0.343770i −0.0144882 0.0144882i 0.699826 0.714314i \(-0.253261\pi\)
−0.714314 + 0.699826i \(0.753261\pi\)
\(564\) 2.71706 4.30869i 0.114409 0.181429i
\(565\) 4.57306 + 28.5126i 0.192390 + 1.19953i
\(566\) 12.7397 + 3.68140i 0.535489 + 0.154741i
\(567\) 1.58415 1.58415i 0.0665282 0.0665282i
\(568\) 25.9698 + 1.52166i 1.08967 + 0.0638473i
\(569\) 14.2062i 0.595555i −0.954635 0.297777i \(-0.903755\pi\)
0.954635 0.297777i \(-0.0962453\pi\)
\(570\) 1.74317 1.36163i 0.0730134 0.0570323i
\(571\) 19.1090i 0.799688i 0.916583 + 0.399844i \(0.130936\pi\)
−0.916583 + 0.399844i \(0.869064\pi\)
\(572\) −2.34004 + 0.530117i −0.0978418 + 0.0221653i
\(573\) −2.04231 + 2.04231i −0.0853187 + 0.0853187i
\(574\) 1.90637 6.59710i 0.0795704 0.275357i
\(575\) −1.81588 + 3.59855i −0.0757276 + 0.150070i
\(576\) −2.34574 + 19.9484i −0.0977393 + 0.831184i
\(577\) −25.4221 25.4221i −1.05834 1.05834i −0.998190 0.0601462i \(-0.980843\pi\)
−0.0601462 0.998190i \(-0.519157\pi\)
\(578\) 7.46820 + 13.5385i 0.310636 + 0.563129i
\(579\) 5.48183 0.227817
\(580\) −7.68411 + 3.08531i −0.319065 + 0.128111i
\(581\) 1.29920 0.0538999
\(582\) 2.79572 + 5.06815i 0.115886 + 0.210082i
\(583\) −16.7331 16.7331i −0.693014 0.693014i
\(584\) −12.8371 14.4351i −0.531203 0.597327i
\(585\) −2.25555 + 0.361762i −0.0932556 + 0.0149570i
\(586\) 8.02363 27.7662i 0.331453 1.14701i
\(587\) −29.3478 + 29.3478i −1.21131 + 1.21131i −0.240717 + 0.970595i \(0.577383\pi\)
−0.970595 + 0.240717i \(0.922617\pi\)
\(588\) 2.09729 + 9.25785i 0.0864909 + 0.381787i
\(589\) 1.12279i 0.0462637i
\(590\) 5.44789 44.3320i 0.224286 1.82512i
\(591\) 5.79788i 0.238493i
\(592\) 7.69919 21.7768i 0.316435 0.895019i
\(593\) 4.78725 4.78725i 0.196589 0.196589i −0.601947 0.798536i \(-0.705608\pi\)
0.798536 + 0.601947i \(0.205608\pi\)
\(594\) 15.4404 + 4.46184i 0.633529 + 0.183072i
\(595\) 1.49570 2.06714i 0.0613178 0.0847443i
\(596\) 22.1846 + 13.9896i 0.908718 + 0.573038i
\(597\) 7.29404 + 7.29404i 0.298525 + 0.298525i
\(598\) 0.406188 0.224064i 0.0166103 0.00916265i
\(599\) −8.94617 −0.365531 −0.182765 0.983157i \(-0.558505\pi\)
−0.182765 + 0.983157i \(0.558505\pi\)
\(600\) 8.55560 + 4.96540i 0.349281 + 0.202711i
\(601\) −31.5967 −1.28886 −0.644429 0.764664i \(-0.722905\pi\)
−0.644429 + 0.764664i \(0.722905\pi\)
\(602\) 5.75815 3.17634i 0.234685 0.129458i
\(603\) 23.8819 + 23.8819i 0.972548 + 0.972548i
\(604\) 3.82325 + 2.41094i 0.155566 + 0.0980998i
\(605\) 3.02438 4.17985i 0.122959 0.169935i
\(606\) −4.37736 1.26493i −0.177818 0.0513844i
\(607\) 5.75786 5.75786i 0.233704 0.233704i −0.580533 0.814237i \(-0.697156\pi\)
0.814237 + 0.580533i \(0.197156\pi\)
\(608\) −4.60023 3.29209i −0.186564 0.133512i
\(609\) 0.599980i 0.0243124i
\(610\) −2.96782 + 24.1505i −0.120163 + 0.977826i
\(611\) 1.48158i 0.0599383i
\(612\) 2.73271 + 12.0627i 0.110463 + 0.487607i
\(613\) −24.9646 + 24.9646i −1.00831 + 1.00831i −0.00834470 + 0.999965i \(0.502656\pi\)
−0.999965 + 0.00834470i \(0.997344\pi\)
\(614\) 6.31016 21.8366i 0.254657 0.881255i
\(615\) 16.1870 2.59620i 0.652724 0.104689i
\(616\) −2.88683 + 2.56726i −0.116314 + 0.103438i
\(617\) 27.5683 + 27.5683i 1.10986 + 1.10986i 0.993168 + 0.116689i \(0.0372281\pi\)
0.116689 + 0.993168i \(0.462772\pi\)
\(618\) −7.31312 13.2574i −0.294177 0.533291i
\(619\) 36.0285 1.44811 0.724054 0.689743i \(-0.242277\pi\)
0.724054 + 0.689743i \(0.242277\pi\)
\(620\) 4.65968 1.87095i 0.187137 0.0751391i
\(621\) −3.10742 −0.124696
\(622\) 21.6087 + 39.1728i 0.866429 + 1.57068i
\(623\) −0.745448 0.745448i −0.0298658 0.0298658i
\(624\) −0.490636 1.02731i −0.0196412 0.0411251i
\(625\) −20.1100 + 14.8522i −0.804400 + 0.594088i
\(626\) 2.28308 7.90072i 0.0912503 0.315776i
\(627\) −1.45826 + 1.45826i −0.0582374 + 0.0582374i
\(628\) −31.6139 + 7.16188i −1.26153 + 0.285790i
\(629\) 14.2230i 0.567109i
\(630\) −2.89865 + 2.26420i −0.115485 + 0.0902078i
\(631\) 20.6862i 0.823504i −0.911296 0.411752i \(-0.864917\pi\)
0.911296 0.411752i \(-0.135083\pi\)
\(632\) 0.0271535 0.463424i 0.00108011 0.0184340i
\(633\) −1.70156 + 1.70156i −0.0676308 + 0.0676308i
\(634\) −41.0594 11.8650i −1.63068 0.471219i
\(635\) −0.179887 1.12158i −0.00713859 0.0445084i
\(636\) 5.98922 9.49766i 0.237488 0.376607i
\(637\) 1.95228 + 1.95228i 0.0773522 + 0.0773522i
\(638\) 6.75991 3.72893i 0.267627 0.147630i
\(639\) −23.0923 −0.913519
\(640\) 5.99694 24.5772i 0.237050 0.971497i
\(641\) −5.19156 −0.205054 −0.102527 0.994730i \(-0.532693\pi\)
−0.102527 + 0.994730i \(0.532693\pi\)
\(642\) 6.25808 3.45211i 0.246987 0.136244i
\(643\) 6.88159 + 6.88159i 0.271384 + 0.271384i 0.829657 0.558273i \(-0.188536\pi\)
−0.558273 + 0.829657i \(0.688536\pi\)
\(644\) 0.398409 0.631794i 0.0156995 0.0248962i
\(645\) 12.7191 + 9.20309i 0.500815 + 0.362371i
\(646\) −3.34643 0.967023i −0.131664 0.0380470i
\(647\) 20.2501 20.2501i 0.796113 0.796113i −0.186368 0.982480i \(-0.559672\pi\)
0.982480 + 0.186368i \(0.0596715\pi\)
\(648\) 0.800080 13.6548i 0.0314301 0.536410i
\(649\) 41.6438i 1.63466i
\(650\) 2.87524 0.105734i 0.112776 0.00414725i
\(651\) 0.363831i 0.0142597i
\(652\) −28.9598 + 6.56062i −1.13415 + 0.256934i
\(653\) 10.5859 10.5859i 0.414257 0.414257i −0.468961 0.883219i \(-0.655372\pi\)
0.883219 + 0.468961i \(0.155372\pi\)
\(654\) 1.43908 4.98000i 0.0562723 0.194733i
\(655\) −12.8188 9.27519i −0.500871 0.362411i
\(656\) −18.0687 37.8328i −0.705466 1.47712i
\(657\) 12.1252 + 12.1252i 0.473049 + 0.473049i
\(658\) −1.15224 2.08881i −0.0449190 0.0814303i
\(659\) −29.9506 −1.16671 −0.583354 0.812218i \(-0.698260\pi\)
−0.583354 + 0.812218i \(0.698260\pi\)
\(660\) −8.48189 3.62197i −0.330157 0.140985i
\(661\) −42.9876 −1.67202 −0.836012 0.548711i \(-0.815119\pi\)
−0.836012 + 0.548711i \(0.815119\pi\)
\(662\) 19.6826 + 35.6811i 0.764985 + 1.38678i
\(663\) −0.495705 0.495705i −0.0192516 0.0192516i
\(664\) 5.92738 5.27121i 0.230027 0.204563i
\(665\) −0.164047 1.02282i −0.00636147 0.0396632i
\(666\) −5.69199 + 19.6974i −0.220560 + 0.763259i
\(667\) −1.05545 + 1.05545i −0.0408671 + 0.0408671i
\(668\) −9.98603 44.0803i −0.386371 1.70552i
\(669\) 9.85422i 0.380986i
\(670\) −26.1860 33.5236i −1.01165 1.29513i
\(671\) 22.6860i 0.875785i
\(672\) −1.49067 1.06678i −0.0575039 0.0411518i
\(673\) 8.30925 8.30925i 0.320298 0.320298i −0.528583 0.848881i \(-0.677277\pi\)
0.848881 + 0.528583i \(0.177277\pi\)
\(674\) 25.8196 + 7.46113i 0.994535 + 0.287392i
\(675\) −17.2065 8.68267i −0.662280 0.334196i
\(676\) 21.7123 + 13.6918i 0.835090 + 0.526608i
\(677\) 1.65901 + 1.65901i 0.0637610 + 0.0637610i 0.738268 0.674507i \(-0.235644\pi\)
−0.674507 + 0.738268i \(0.735644\pi\)
\(678\) 11.1858 6.17038i 0.429589 0.236972i
\(679\) 2.71067 0.104026
\(680\) −1.56306 15.4994i −0.0599405 0.594376i
\(681\) −8.35673 −0.320230
\(682\) −4.09924 + 2.26125i −0.156968 + 0.0865875i
\(683\) 3.72871 + 3.72871i 0.142675 + 0.142675i 0.774837 0.632161i \(-0.217832\pi\)
−0.632161 + 0.774837i \(0.717832\pi\)
\(684\) 4.24747 + 2.67846i 0.162406 + 0.102413i
\(685\) 13.5122 2.16718i 0.516273 0.0828036i
\(686\) 8.67655 + 2.50727i 0.331272 + 0.0957282i
\(687\) −4.27345 + 4.27345i −0.163042 + 0.163042i
\(688\) 13.3833 37.8539i 0.510233 1.44317i
\(689\) 3.26585i 0.124419i
\(690\) 1.76985 + 0.217493i 0.0673769 + 0.00827984i
\(691\) 0.815388i 0.0310188i 0.999880 + 0.0155094i \(0.00493700\pi\)
−0.999880 + 0.0155094i \(0.995063\pi\)
\(692\) 7.95538 + 35.1166i 0.302418 + 1.33493i
\(693\) 2.42489 2.42489i 0.0921139 0.0921139i
\(694\) 10.9377 37.8504i 0.415188 1.43678i
\(695\) 14.9884 20.7148i 0.568543 0.785756i
\(696\) 2.43429 + 2.73731i 0.0922714 + 0.103757i
\(697\) −18.2554 18.2554i −0.691474 0.691474i
\(698\) 5.17399 + 9.37955i 0.195839 + 0.355021i
\(699\) −4.49834 −0.170143
\(700\) 3.97144 2.38517i 0.150106 0.0901511i
\(701\) 9.25242 0.349459 0.174730 0.984616i \(-0.444095\pi\)
0.174730 + 0.984616i \(0.444095\pi\)
\(702\) 1.07136 + 1.94220i 0.0404360 + 0.0733035i
\(703\) −4.08314 4.08314i −0.153999 0.153999i
\(704\) −2.75459 + 23.4253i −0.103818 + 0.882875i
\(705\) 3.33848 4.61396i 0.125735 0.173772i
\(706\) 6.83798 23.6632i 0.257351 0.890576i
\(707\) −1.50888 + 1.50888i −0.0567471 + 0.0567471i
\(708\) −19.2712 + 4.36573i −0.724255 + 0.164074i
\(709\) 25.0837i 0.942038i 0.882123 + 0.471019i \(0.156114\pi\)
−0.882123 + 0.471019i \(0.843886\pi\)
\(710\) 28.8677 + 3.54751i 1.08339 + 0.133136i
\(711\) 0.412076i 0.0154541i
\(712\) −6.42547 0.376490i −0.240805 0.0141096i
\(713\) 0.640030 0.640030i 0.0239693 0.0239693i
\(714\) −1.08439 0.313357i −0.0405822 0.0117271i
\(715\) −2.64868 + 0.424815i −0.0990551 + 0.0158872i
\(716\) 3.81829 6.05501i 0.142696 0.226286i
\(717\) 11.4239 + 11.4239i 0.426634 + 0.426634i
\(718\) −29.0450 + 16.0220i −1.08395 + 0.597934i
\(719\) 37.6238 1.40313 0.701565 0.712606i \(-0.252485\pi\)
0.701565 + 0.712606i \(0.252485\pi\)
\(720\) −4.03812 + 22.0906i −0.150492 + 0.823269i
\(721\) −7.09065 −0.264070
\(722\) −1.23831 + 0.683080i −0.0460850 + 0.0254216i
\(723\) 9.81405 + 9.81405i 0.364988 + 0.364988i
\(724\) −7.89954 + 12.5270i −0.293584 + 0.465563i
\(725\) −8.79340 + 2.89517i −0.326579 + 0.107524i
\(726\) −2.19268 0.633622i −0.0813780 0.0235159i
\(727\) −27.9775 + 27.9775i −1.03763 + 1.03763i −0.0383634 + 0.999264i \(0.512214\pi\)
−0.999264 + 0.0383634i \(0.987786\pi\)
\(728\) −0.532246 0.0311861i −0.0197263 0.00115583i
\(729\) 4.05317i 0.150117i
\(730\) −13.2950 17.0204i −0.492071 0.629954i
\(731\) 24.7235i 0.914430i
\(732\) 10.4982 2.37829i 0.388026 0.0879043i
\(733\) 13.9853 13.9853i 0.516559 0.516559i −0.399970 0.916528i \(-0.630979\pi\)
0.916528 + 0.399970i \(0.130979\pi\)
\(734\) −12.9681 + 44.8767i −0.478661 + 1.65643i
\(735\) 1.68069 + 10.4789i 0.0619932 + 0.386522i
\(736\) −0.745687 4.49890i −0.0274864 0.165832i
\(737\) 28.0444 + 28.0444i 1.03303 + 1.03303i
\(738\) 17.9762 + 32.5876i 0.661711 + 1.19957i
\(739\) 40.9090 1.50486 0.752431 0.658671i \(-0.228881\pi\)
0.752431 + 0.658671i \(0.228881\pi\)
\(740\) 10.1415 23.7493i 0.372810 0.873043i
\(741\) −0.284614 −0.0104555
\(742\) −2.53988 4.60437i −0.0932421 0.169032i
\(743\) 4.46740 + 4.46740i 0.163893 + 0.163893i 0.784289 0.620396i \(-0.213028\pi\)
−0.620396 + 0.784289i \(0.713028\pi\)
\(744\) −1.47616 1.65992i −0.0541188 0.0608555i
\(745\) 23.7564 + 17.1892i 0.870366 + 0.629764i
\(746\) −3.40105 + 11.7695i −0.124521 + 0.430912i
\(747\) −4.97890 + 4.97890i −0.182168 + 0.182168i
\(748\) 3.20901 + 14.1652i 0.117333 + 0.517931i
\(749\) 3.34710i 0.122300i
\(750\) 9.19237 + 6.14958i 0.335658 + 0.224551i
\(751\) 37.1200i 1.35453i 0.735740 + 0.677264i \(0.236834\pi\)
−0.735740 + 0.677264i \(0.763166\pi\)
\(752\) −13.7318 4.85488i −0.500746 0.177039i
\(753\) 2.88223 2.88223i 0.105034 0.105034i
\(754\) 1.02357 + 0.295782i 0.0372762 + 0.0107718i
\(755\) 4.09412 + 2.96235i 0.149000 + 0.107811i
\(756\) 3.02093 + 1.90500i 0.109870 + 0.0692842i
\(757\) 17.9260 + 17.9260i 0.651533 + 0.651533i 0.953362 0.301829i \(-0.0975972\pi\)
−0.301829 + 0.953362i \(0.597597\pi\)
\(758\) 28.4456 15.6913i 1.03319 0.569934i
\(759\) −1.66252 −0.0603458
\(760\) −4.89829 4.00085i −0.177680 0.145126i
\(761\) −31.7582 −1.15123 −0.575617 0.817719i \(-0.695238\pi\)
−0.575617 + 0.817719i \(0.695238\pi\)
\(762\) −0.440008 + 0.242719i −0.0159398 + 0.00879279i
\(763\) −1.71660 1.71660i −0.0621452 0.0621452i
\(764\) 6.98543 + 4.40501i 0.252724 + 0.159368i
\(765\) 2.18989 + 13.6538i 0.0791757 + 0.493653i
\(766\) 35.6503 + 10.3019i 1.28810 + 0.372224i
\(767\) −4.06387 + 4.06387i −0.146738 + 0.146738i
\(768\) −11.1291 + 1.18107i −0.401588 + 0.0426184i
\(769\) 32.9935i 1.18977i 0.803809 + 0.594887i \(0.202803\pi\)
−0.803809 + 0.594887i \(0.797197\pi\)
\(770\) −3.40387 + 2.65883i −0.122667 + 0.0958177i
\(771\) 6.12270i 0.220504i
\(772\) −3.46309 15.2867i −0.124639 0.550182i
\(773\) −13.8810 + 13.8810i −0.499265 + 0.499265i −0.911209 0.411944i \(-0.864850\pi\)
0.411944 + 0.911209i \(0.364850\pi\)
\(774\) −9.89422 + 34.2394i −0.355640 + 1.23071i
\(775\) 5.33236 1.75565i 0.191544 0.0630648i
\(776\) 12.3670 10.9979i 0.443948 0.394803i
\(777\) −1.32311 1.32311i −0.0474663 0.0474663i
\(778\) 25.4250 + 46.0911i 0.911530 + 1.65244i
\(779\) −10.4815 −0.375540
\(780\) −0.474263 1.18117i −0.0169814 0.0422928i
\(781\) −27.1172 −0.970330
\(782\) −1.35635 2.45882i −0.0485029 0.0879274i
\(783\) −5.04665 5.04665i −0.180352 0.180352i
\(784\) 24.4917 11.6971i 0.874702 0.417753i
\(785\) −35.7837 + 5.73926i −1.27718 + 0.204843i
\(786\) −1.94320 + 6.72453i −0.0693115 + 0.239856i
\(787\) 28.4639 28.4639i 1.01463 1.01463i 0.0147356 0.999891i \(-0.495309\pi\)
0.999891 0.0147356i \(-0.00469066\pi\)
\(788\) 16.1681 3.66275i 0.575963 0.130480i
\(789\) 8.35948i 0.297605i
\(790\) 0.0633043 0.515137i 0.00225227 0.0183277i
\(791\) 5.98267i 0.212719i
\(792\) 1.22469 20.9016i 0.0435176 0.742705i
\(793\) 2.21385 2.21385i 0.0786163 0.0786163i
\(794\) −15.7865 4.56185i −0.560243 0.161894i
\(795\) 7.35903 10.1705i 0.260998 0.360712i
\(796\) 15.7324 24.9482i 0.557619 0.884266i
\(797\) 20.8840 + 20.8840i 0.739750 + 0.739750i 0.972530 0.232779i \(-0.0747820\pi\)
−0.232779 + 0.972530i \(0.574782\pi\)
\(798\) −0.401264 + 0.221347i −0.0142046 + 0.00783560i
\(799\) −8.96861 −0.317287
\(800\) 8.44168 26.9951i 0.298458 0.954423i
\(801\) 5.71353 0.201878
\(802\) −35.4013 + 19.5283i −1.25006 + 0.689567i
\(803\) 14.2386 + 14.2386i 0.502468 + 0.502468i
\(804\) −10.0379 + 15.9180i −0.354008 + 0.561383i
\(805\) 0.489530 0.676555i 0.0172537 0.0238454i
\(806\) −0.620698 0.179364i −0.0218632 0.00631783i
\(807\) 0.743195 0.743195i 0.0261617 0.0261617i
\(808\) −0.762060 + 13.0059i −0.0268092 + 0.457546i
\(809\) 23.6436i 0.831266i −0.909532 0.415633i \(-0.863560\pi\)
0.909532 0.415633i \(-0.136440\pi\)
\(810\) 1.86526 15.1785i 0.0655387 0.533319i
\(811\) 2.24873i 0.0789635i −0.999220 0.0394817i \(-0.987429\pi\)
0.999220 0.0394817i \(-0.0125707\pi\)
\(812\) 1.67312 0.379031i 0.0587149 0.0133014i
\(813\) −14.6496 + 14.6496i −0.513783 + 0.513783i
\(814\) −6.68407 + 23.1306i −0.234277 + 0.810726i
\(815\) −32.7796 + 5.25743i −1.14822 + 0.184160i
\(816\) −6.21870 + 2.97002i −0.217698 + 0.103971i
\(817\) −7.09760 7.09760i −0.248314 0.248314i
\(818\) −5.73828 10.4025i −0.200634 0.363715i
\(819\) 0.473273 0.0165375
\(820\) −17.4658 43.4994i −0.609932 1.51906i
\(821\) −26.4934 −0.924625 −0.462312 0.886717i \(-0.652980\pi\)
−0.462312 + 0.886717i \(0.652980\pi\)
\(822\) −2.92415 5.30098i −0.101991 0.184893i
\(823\) −34.3245 34.3245i −1.19648 1.19648i −0.975214 0.221262i \(-0.928982\pi\)
−0.221262 0.975214i \(-0.571018\pi\)
\(824\) −32.3499 + 28.7687i −1.12696 + 1.00221i
\(825\) −9.20581 4.64538i −0.320505 0.161732i
\(826\) −2.56895 + 8.88998i −0.0893851 + 0.309322i
\(827\) −27.3304 + 27.3304i −0.950371 + 0.950371i −0.998825 0.0484541i \(-0.984571\pi\)
0.0484541 + 0.998825i \(0.484571\pi\)
\(828\) 0.894393 + 3.94802i 0.0310823 + 0.137203i
\(829\) 27.1022i 0.941297i 0.882321 + 0.470648i \(0.155980\pi\)
−0.882321 + 0.470648i \(0.844020\pi\)
\(830\) 6.98899 5.45925i 0.242591 0.189493i
\(831\) 18.0398i 0.625793i
\(832\) −2.55481 + 2.01719i −0.0885720 + 0.0699333i
\(833\) 11.8180 11.8180i 0.409468 0.409468i
\(834\) −10.8666 3.14015i −0.376281 0.108734i
\(835\) −8.00242 49.8944i −0.276935 1.72667i
\(836\) 4.98778 + 3.14530i 0.172506 + 0.108782i
\(837\) 3.06031 + 3.06031i 0.105780 + 0.105780i
\(838\) 17.7031 9.76546i 0.611543 0.337342i
\(839\) −32.8801 −1.13515 −0.567573 0.823323i \(-0.692118\pi\)
−0.567573 + 0.823323i \(0.692118\pi\)
\(840\) −1.58725 1.29644i −0.0547654 0.0447315i
\(841\) 25.5718 0.881785
\(842\) −49.6256 + 27.3747i −1.71021 + 0.943396i
\(843\) 8.03613 + 8.03613i 0.276779 + 0.276779i
\(844\) 5.81994 + 3.67005i 0.200330 + 0.126328i
\(845\) 23.2506 + 16.8233i 0.799846 + 0.578738i
\(846\) 12.4206 + 3.58920i 0.427029 + 0.123399i
\(847\) −0.755816 + 0.755816i −0.0259701 + 0.0259701i
\(848\) −30.2690 10.7016i −1.03944 0.367495i
\(849\) 6.55891i 0.225101i
\(850\) −0.640054 17.4050i −0.0219537 0.596987i
\(851\) 4.65507i 0.159574i
\(852\) −2.84284 12.5488i −0.0973940 0.429916i
\(853\) 20.4055 20.4055i 0.698672 0.698672i −0.265452 0.964124i \(-0.585521\pi\)
0.964124 + 0.265452i \(0.0855212\pi\)
\(854\) 1.39947 4.84295i 0.0478889 0.165722i
\(855\) 4.54839 + 3.29105i 0.155552 + 0.112551i
\(856\) −13.5801 15.2706i −0.464158 0.521937i
\(857\) 2.57518 + 2.57518i 0.0879665 + 0.0879665i 0.749721 0.661754i \(-0.230188\pi\)
−0.661754 + 0.749721i \(0.730188\pi\)
\(858\) 0.573199 + 1.03911i 0.0195687 + 0.0354746i
\(859\) −48.7635 −1.66379 −0.831895 0.554933i \(-0.812744\pi\)
−0.831895 + 0.554933i \(0.812744\pi\)
\(860\) 17.6287 41.2828i 0.601134 1.40773i
\(861\) −3.39646 −0.115751
\(862\) −20.6977 37.5213i −0.704965 1.27798i
\(863\) −0.809522 0.809522i −0.0275565 0.0275565i 0.693194 0.720751i \(-0.256203\pi\)
−0.720751 + 0.693194i \(0.756203\pi\)
\(864\) 21.5116 3.56552i 0.731839 0.121301i
\(865\) 6.37514 + 39.7484i 0.216761 + 1.35149i
\(866\) −2.31434 + 8.00890i −0.0786445 + 0.272154i
\(867\) 5.40757 5.40757i 0.183651 0.183651i
\(868\) −1.01459 + 0.229847i −0.0344373 + 0.00780150i
\(869\) 0.483899i 0.0164152i
\(870\) 2.52112 + 3.22757i 0.0854740 + 0.109425i
\(871\) 5.47352i 0.185463i
\(872\) −14.7964 0.866973i −0.501071 0.0293594i
\(873\) −10.3880 + 10.3880i −0.351582 + 0.351582i
\(874\) −1.09526 0.316498i −0.0370477 0.0107057i
\(875\) 4.60107 2.37842i 0.155544 0.0804054i
\(876\) −5.09637 + 8.08177i −0.172190 + 0.273058i
\(877\) −18.6769 18.6769i −0.630676 0.630676i 0.317562 0.948238i \(-0.397136\pi\)
−0.948238 + 0.317562i \(0.897136\pi\)
\(878\) −23.9538 + 13.2135i −0.808403 + 0.445935i
\(879\) −14.2952 −0.482165
\(880\) −4.74195 + 25.9409i −0.159851 + 0.874468i
\(881\) −33.9283 −1.14307 −0.571536 0.820577i \(-0.693652\pi\)
−0.571536 + 0.820577i \(0.693652\pi\)
\(882\) −21.0961 + 11.6372i −0.710344 + 0.391843i
\(883\) 16.3593 + 16.3593i 0.550535 + 0.550535i 0.926595 0.376060i \(-0.122721\pi\)
−0.376060 + 0.926595i \(0.622721\pi\)
\(884\) −1.06918 + 1.69549i −0.0359603 + 0.0570255i
\(885\) −21.8130 + 3.49853i −0.733236 + 0.117602i
\(886\) 7.99147 + 2.30931i 0.268479 + 0.0775827i
\(887\) −33.6480 + 33.6480i −1.12979 + 1.12979i −0.139579 + 0.990211i \(0.544575\pi\)
−0.990211 + 0.139579i \(0.955425\pi\)
\(888\) −11.4047 0.668239i −0.382716 0.0224246i
\(889\) 0.235336i 0.00789291i
\(890\) −7.14248 0.877728i −0.239417 0.0294215i
\(891\) 14.2581i 0.477664i
\(892\) 27.4797 6.22530i 0.920087 0.208438i
\(893\) −2.57471 + 2.57471i −0.0861592 + 0.0861592i
\(894\) 3.60122 12.4622i 0.120443 0.416799i
\(895\) 4.69158 6.48400i 0.156822 0.216736i
\(896\) −2.03312 + 4.83084i −0.0679217 + 0.161387i
\(897\) −0.162240 0.162240i −0.00541703 0.00541703i
\(898\) −15.1388 27.4441i −0.505189 0.915820i
\(899\) 2.07890 0.0693352
\(900\) −6.07899 + 24.3603i −0.202633 + 0.812010i
\(901\) −19.7695 −0.658618
\(902\) 21.1093 + 38.2675i 0.702863 + 1.27417i
\(903\) −2.29992 2.29992i −0.0765367 0.0765367i
\(904\) −24.2734 27.2949i −0.807320 0.907815i
\(905\) −9.70625 + 13.4145i −0.322647 + 0.445914i
\(906\) 0.620626 2.14771i 0.0206189 0.0713529i
\(907\) 9.92358 9.92358i 0.329507 0.329507i −0.522892 0.852399i \(-0.675147\pi\)
0.852399 + 0.522892i \(0.175147\pi\)
\(908\) 5.27927 + 23.3037i 0.175199 + 0.773361i
\(909\) 11.5649i 0.383582i
\(910\) −0.591639 0.0727055i −0.0196126 0.00241016i
\(911\) 32.8155i 1.08722i 0.839337 + 0.543612i \(0.182944\pi\)
−0.839337 + 0.543612i \(0.817056\pi\)
\(912\) −0.932630 + 2.63789i −0.0308825 + 0.0873494i
\(913\) −5.84669 + 5.84669i −0.193497 + 0.193497i
\(914\) −20.8374 6.02141i −0.689240 0.199171i
\(915\) 11.8829 1.90587i 0.392838 0.0630063i
\(916\) 14.6167 + 9.21731i 0.482950 + 0.304549i
\(917\) 2.31794 + 2.31794i 0.0765452 + 0.0765452i
\(918\) 11.7569 6.48540i 0.388036 0.214050i
\(919\) 13.4713 0.444377 0.222188 0.975004i \(-0.428680\pi\)
0.222188 + 0.975004i \(0.428680\pi\)
\(920\) −0.511575 5.07282i −0.0168661 0.167246i
\(921\) −11.2424 −0.370450
\(922\) 7.79668 4.30084i 0.256770 0.141641i
\(923\) −2.64628 2.64628i −0.0871032 0.0871032i
\(924\) 1.61625 + 1.01921i 0.0531708 + 0.0335295i
\(925\) 13.0071 25.7763i 0.427670 0.847519i
\(926\) −10.7746 3.11356i −0.354077 0.102318i
\(927\) 27.1733 27.1733i 0.892489 0.892489i
\(928\) 6.09547 8.51756i 0.200094 0.279603i
\(929\) 30.3568i 0.995973i −0.867185 0.497987i \(-0.834073\pi\)
0.867185 0.497987i \(-0.165927\pi\)
\(930\) −1.52882 1.95721i −0.0501320 0.0641796i
\(931\) 6.78539i 0.222382i
\(932\) 2.84178 + 12.5442i 0.0930855 + 0.410897i
\(933\) 15.6464 15.6464i 0.512240 0.512240i
\(934\) −13.1427 + 45.4810i −0.430042 + 1.48818i
\(935\) 2.57158 + 16.0336i 0.0840996 + 0.524353i
\(936\) 2.15923 1.92020i 0.0705765 0.0627637i
\(937\) −27.4311 27.4311i −0.896135 0.896135i 0.0989565 0.995092i \(-0.468450\pi\)
−0.995092 + 0.0989565i \(0.968450\pi\)
\(938\) 4.25681 + 7.71686i 0.138990 + 0.251964i
\(939\) −4.06762 −0.132742
\(940\) −14.9756 6.39494i −0.488451 0.208580i
\(941\) 12.9566 0.422372 0.211186 0.977446i \(-0.432267\pi\)
0.211186 + 0.977446i \(0.432267\pi\)
\(942\) 7.74392 + 14.0384i 0.252311 + 0.457395i
\(943\) −5.97484 5.97484i −0.194568 0.194568i
\(944\) 24.3487 + 50.9819i 0.792483 + 1.65932i
\(945\) 3.23496 + 2.34070i 0.105233 + 0.0761428i
\(946\) −11.6187 + 40.2072i −0.377757 + 1.30725i
\(947\) −22.3305 + 22.3305i −0.725642 + 0.725642i −0.969748 0.244106i \(-0.921505\pi\)
0.244106 + 0.969748i \(0.421505\pi\)
\(948\) −0.223930 + 0.0507296i −0.00727292 + 0.00164762i
\(949\) 2.77899i 0.0902097i
\(950\) −5.18037 4.81288i −0.168073 0.156150i
\(951\) 21.1391i 0.685483i
\(952\) −0.188782 + 3.22190i −0.00611846 + 0.104422i
\(953\) 1.79070 1.79070i 0.0580064 0.0580064i −0.677509 0.735515i \(-0.736940\pi\)
0.735515 + 0.677509i \(0.236940\pi\)
\(954\) 27.3787 + 7.91167i 0.886420 + 0.256150i
\(955\) 7.48033 + 5.41249i 0.242058 + 0.175144i
\(956\) 24.6400 39.0739i 0.796915 1.26374i
\(957\) −2.70005 2.70005i −0.0872801 0.0872801i
\(958\) −15.8507 + 8.74367i −0.512114 + 0.282495i
\(959\) −2.83520 −0.0915533
\(960\) −12.5016 + 0.525125i −0.403487 + 0.0169483i
\(961\) 29.7393 0.959334
\(962\) −2.90951 + 1.60496i −0.0938063 + 0.0517459i
\(963\) 12.8270 + 12.8270i 0.413344 + 0.413344i
\(964\) 21.1677 33.5676i 0.681766 1.08114i
\(965\) −2.77519 17.3030i −0.0893364 0.557004i
\(966\) −0.354910 0.102559i −0.0114190 0.00329978i
\(967\) −11.6241 + 11.6241i −0.373807 + 0.373807i −0.868862 0.495055i \(-0.835148\pi\)
0.495055 + 0.868862i \(0.335148\pi\)
\(968\) −0.381726 + 6.51483i −0.0122691 + 0.209395i
\(969\) 1.72288i 0.0553470i
\(970\) 14.5819 11.3903i 0.468198 0.365719i
\(971\) 16.0160i 0.513977i 0.966415 + 0.256988i \(0.0827302\pi\)
−0.966415 + 0.256988i \(0.917270\pi\)
\(972\) −29.1543 + 6.60468i −0.935125 + 0.211845i
\(973\) −3.74573 + 3.74573i −0.120082 + 0.120082i
\(974\) −5.96973 + 20.6586i −0.191282 + 0.661943i
\(975\) −0.445036 1.35169i −0.0142526 0.0432887i
\(976\) −13.2643 27.7731i −0.424580 0.888996i
\(977\) 10.3212 + 10.3212i 0.330205 + 0.330205i 0.852664 0.522459i \(-0.174985\pi\)
−0.522459 + 0.852664i \(0.674985\pi\)
\(978\) 7.09379 + 12.8598i 0.226834 + 0.411211i
\(979\) 6.70937 0.214432
\(980\) 28.1600 11.3068i 0.899539 0.361181i
\(981\) 13.1570 0.420071
\(982\) −26.8253 48.6296i −0.856031 1.55183i
\(983\) −20.0695 20.0695i −0.640119 0.640119i 0.310466 0.950585i \(-0.399515\pi\)
−0.950585 + 0.310466i \(0.899515\pi\)
\(984\) −15.4958 + 13.7804i −0.493987 + 0.439302i
\(985\) 18.3006 2.93519i 0.583106 0.0935228i
\(986\) 1.79049 6.19609i 0.0570209 0.197324i
\(987\) −0.834314 + 0.834314i −0.0265565 + 0.0265565i
\(988\) 0.179802 + 0.793679i 0.00572025 + 0.0252503i
\(989\) 8.09177i 0.257303i
\(990\) 2.85518 23.2340i 0.0907437 0.738424i
\(991\) 59.6794i 1.89578i 0.318599 + 0.947890i \(0.396788\pi\)
−0.318599 + 0.947890i \(0.603212\pi\)
\(992\) −3.69632 + 5.16509i −0.117358 + 0.163992i
\(993\) 14.2518 14.2518i 0.452266 0.452266i
\(994\) −5.78890 1.67282i −0.183613 0.0530588i
\(995\) 19.3305 26.7158i 0.612819 0.846947i
\(996\) −3.31857 2.09269i −0.105153 0.0663094i
\(997\) −8.77680 8.77680i −0.277964 0.277964i 0.554332 0.832296i \(-0.312974\pi\)
−0.832296 + 0.554332i \(0.812974\pi\)
\(998\) 44.3953 24.4896i 1.40531 0.775204i
\(999\) 22.2583 0.704221
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 380.2.k.d.267.5 yes 52
4.3 odd 2 380.2.k.c.267.19 52
5.3 odd 4 380.2.k.c.343.19 yes 52
20.3 even 4 inner 380.2.k.d.343.5 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.k.c.267.19 52 4.3 odd 2
380.2.k.c.343.19 yes 52 5.3 odd 4
380.2.k.d.267.5 yes 52 1.1 even 1 trivial
380.2.k.d.343.5 yes 52 20.3 even 4 inner