Properties

Label 630.2.t.c.311.4
Level $630$
Weight $2$
Character 630.311
Analytic conductor $5.031$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(311,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.311");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 311.4
Character \(\chi\) \(=\) 630.311
Dual form 630.2.t.c.551.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.423533 + 1.67947i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.20653 - 1.24270i) q^{6} +(2.20024 - 1.46933i) q^{7} -1.00000i q^{8} +(-2.64124 - 1.42262i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.423533 + 1.67947i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.20653 - 1.24270i) q^{6} +(2.20024 - 1.46933i) q^{7} -1.00000i q^{8} +(-2.64124 - 1.42262i) q^{9} +(-0.866025 - 0.500000i) q^{10} -4.43825i q^{11} +(-1.66623 + 0.472945i) q^{12} +(-4.51990 - 2.60957i) q^{13} +(-2.64013 + 0.172355i) q^{14} +(-0.423533 + 1.67947i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.46981 - 6.00989i) q^{17} +(1.57607 + 2.55265i) q^{18} +(-2.43077 + 1.40341i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.53582 + 4.31755i) q^{21} +(-2.21912 + 3.84363i) q^{22} -3.48491i q^{23} +(1.67947 + 0.423533i) q^{24} +1.00000 q^{25} +(2.60957 + 4.51990i) q^{26} +(3.50790 - 3.83336i) q^{27} +(2.37260 + 1.17080i) q^{28} +(-6.40344 + 3.69703i) q^{29} +(1.20653 - 1.24270i) q^{30} +(-1.82054 + 1.05109i) q^{31} +(0.866025 - 0.500000i) q^{32} +(7.45390 + 1.87974i) q^{33} +(-6.00989 + 3.46981i) q^{34} +(2.20024 - 1.46933i) q^{35} +(-0.0885938 - 2.99869i) q^{36} +(4.36995 + 7.56898i) q^{37} +2.80681 q^{38} +(6.29702 - 6.48580i) q^{39} -1.00000i q^{40} +(2.90122 - 5.02506i) q^{41} +(0.828717 - 4.50702i) q^{42} +(-1.02568 - 1.77653i) q^{43} +(3.84363 - 2.21912i) q^{44} +(-2.64124 - 1.42262i) q^{45} +(-1.74245 + 3.01802i) q^{46} +(5.16742 - 8.95023i) q^{47} +(-1.24270 - 1.20653i) q^{48} +(2.68214 - 6.46576i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(8.62385 + 8.37283i) q^{51} -5.21913i q^{52} +(-4.60281 - 2.65743i) q^{53} +(-4.95461 + 1.56583i) q^{54} -4.43825i q^{55} +(-1.46933 - 2.20024i) q^{56} +(-1.32747 - 4.67679i) q^{57} +7.39406 q^{58} +(-0.534861 - 0.926406i) q^{59} +(-1.66623 + 0.472945i) q^{60} +(5.23536 + 3.02264i) q^{61} +2.10218 q^{62} +(-7.90167 + 0.750738i) q^{63} -1.00000 q^{64} +(-4.51990 - 2.60957i) q^{65} +(-5.51540 - 5.35486i) q^{66} +(-2.46400 - 4.26778i) q^{67} +6.93962 q^{68} +(5.85279 + 1.47597i) q^{69} +(-2.64013 + 0.172355i) q^{70} +11.5388i q^{71} +(-1.42262 + 2.64124i) q^{72} +(13.1874 + 7.61374i) q^{73} -8.73991i q^{74} +(-0.423533 + 1.67947i) q^{75} +(-2.43077 - 1.40341i) q^{76} +(-6.52125 - 9.76522i) q^{77} +(-8.69628 + 2.46836i) q^{78} +(-3.88551 + 6.72991i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.95230 + 7.51497i) q^{81} +(-5.02506 + 2.90122i) q^{82} +(-2.84720 - 4.93150i) q^{83} +(-2.97120 + 3.48884i) q^{84} +(3.46981 - 6.00989i) q^{85} +2.05136i q^{86} +(-3.49698 - 12.3202i) q^{87} -4.43825 q^{88} +(4.16961 + 7.22198i) q^{89} +(1.57607 + 2.55265i) q^{90} +(-13.7792 + 0.899543i) q^{91} +(3.01802 - 1.74245i) q^{92} +(-0.994216 - 3.50272i) q^{93} +(-8.95023 + 5.16742i) q^{94} +(-2.43077 + 1.40341i) q^{95} +(0.472945 + 1.66623i) q^{96} +(-11.4765 + 6.62595i) q^{97} +(-5.55569 + 4.25845i) q^{98} +(-6.31395 + 11.7225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.423533 + 1.67947i −0.244527 + 0.969643i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000 0.447214
\(6\) 1.20653 1.24270i 0.492562 0.507329i
\(7\) 2.20024 1.46933i 0.831614 0.555354i
\(8\) 1.00000i 0.353553i
\(9\) −2.64124 1.42262i −0.880413 0.474207i
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) 4.43825i 1.33818i −0.743181 0.669091i \(-0.766684\pi\)
0.743181 0.669091i \(-0.233316\pi\)
\(12\) −1.66623 + 0.472945i −0.480999 + 0.136527i
\(13\) −4.51990 2.60957i −1.25360 0.723763i −0.281773 0.959481i \(-0.590923\pi\)
−0.971822 + 0.235717i \(0.924256\pi\)
\(14\) −2.64013 + 0.172355i −0.705605 + 0.0460638i
\(15\) −0.423533 + 1.67947i −0.109356 + 0.433637i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.46981 6.00989i 0.841552 1.45761i −0.0470295 0.998894i \(-0.514975\pi\)
0.888582 0.458718i \(-0.151691\pi\)
\(18\) 1.57607 + 2.55265i 0.371483 + 0.601664i
\(19\) −2.43077 + 1.40341i −0.557657 + 0.321963i −0.752204 0.658930i \(-0.771009\pi\)
0.194548 + 0.980893i \(0.437676\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 1.53582 + 4.31755i 0.335143 + 0.942167i
\(22\) −2.21912 + 3.84363i −0.473119 + 0.819466i
\(23\) 3.48491i 0.726653i −0.931662 0.363326i \(-0.881641\pi\)
0.931662 0.363326i \(-0.118359\pi\)
\(24\) 1.67947 + 0.423533i 0.342820 + 0.0864533i
\(25\) 1.00000 0.200000
\(26\) 2.60957 + 4.51990i 0.511778 + 0.886426i
\(27\) 3.50790 3.83336i 0.675096 0.737730i
\(28\) 2.37260 + 1.17080i 0.448379 + 0.221261i
\(29\) −6.40344 + 3.69703i −1.18909 + 0.686521i −0.958100 0.286435i \(-0.907530\pi\)
−0.230990 + 0.972956i \(0.574196\pi\)
\(30\) 1.20653 1.24270i 0.220280 0.226884i
\(31\) −1.82054 + 1.05109i −0.326979 + 0.188781i −0.654499 0.756063i \(-0.727120\pi\)
0.327520 + 0.944844i \(0.393787\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 7.45390 + 1.87974i 1.29756 + 0.327221i
\(34\) −6.00989 + 3.46981i −1.03069 + 0.595067i
\(35\) 2.20024 1.46933i 0.371909 0.248362i
\(36\) −0.0885938 2.99869i −0.0147656 0.499782i
\(37\) 4.36995 + 7.56898i 0.718416 + 1.24433i 0.961627 + 0.274359i \(0.0884658\pi\)
−0.243211 + 0.969973i \(0.578201\pi\)
\(38\) 2.80681 0.455325
\(39\) 6.29702 6.48580i 1.00833 1.03856i
\(40\) 1.00000i 0.158114i
\(41\) 2.90122 5.02506i 0.453094 0.784782i −0.545482 0.838122i \(-0.683653\pi\)
0.998576 + 0.0533403i \(0.0169868\pi\)
\(42\) 0.828717 4.50702i 0.127874 0.695448i
\(43\) −1.02568 1.77653i −0.156415 0.270919i 0.777158 0.629305i \(-0.216660\pi\)
−0.933573 + 0.358386i \(0.883327\pi\)
\(44\) 3.84363 2.21912i 0.579450 0.334545i
\(45\) −2.64124 1.42262i −0.393733 0.212072i
\(46\) −1.74245 + 3.01802i −0.256911 + 0.444982i
\(47\) 5.16742 8.95023i 0.753745 1.30552i −0.192251 0.981346i \(-0.561579\pi\)
0.945996 0.324179i \(-0.105088\pi\)
\(48\) −1.24270 1.20653i −0.179368 0.174147i
\(49\) 2.68214 6.46576i 0.383163 0.923681i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 8.62385 + 8.37283i 1.20758 + 1.17243i
\(52\) 5.21913i 0.723763i
\(53\) −4.60281 2.65743i −0.632245 0.365027i 0.149376 0.988780i \(-0.452273\pi\)
−0.781621 + 0.623754i \(0.785607\pi\)
\(54\) −4.95461 + 1.56583i −0.674237 + 0.213083i
\(55\) 4.43825i 0.598453i
\(56\) −1.46933 2.20024i −0.196347 0.294020i
\(57\) −1.32747 4.67679i −0.175827 0.619456i
\(58\) 7.39406 0.970887
\(59\) −0.534861 0.926406i −0.0696329 0.120608i 0.829107 0.559090i \(-0.188849\pi\)
−0.898740 + 0.438482i \(0.855516\pi\)
\(60\) −1.66623 + 0.472945i −0.215109 + 0.0610569i
\(61\) 5.23536 + 3.02264i 0.670319 + 0.387009i 0.796198 0.605037i \(-0.206842\pi\)
−0.125878 + 0.992046i \(0.540175\pi\)
\(62\) 2.10218 0.266977
\(63\) −7.90167 + 0.750738i −0.995517 + 0.0945842i
\(64\) −1.00000 −0.125000
\(65\) −4.51990 2.60957i −0.560625 0.323677i
\(66\) −5.51540 5.35486i −0.678899 0.659137i
\(67\) −2.46400 4.26778i −0.301026 0.521392i 0.675343 0.737504i \(-0.263996\pi\)
−0.976369 + 0.216112i \(0.930662\pi\)
\(68\) 6.93962 0.841552
\(69\) 5.85279 + 1.47597i 0.704594 + 0.177686i
\(70\) −2.64013 + 0.172355i −0.315556 + 0.0206004i
\(71\) 11.5388i 1.36940i 0.728825 + 0.684700i \(0.240067\pi\)
−0.728825 + 0.684700i \(0.759933\pi\)
\(72\) −1.42262 + 2.64124i −0.167658 + 0.311273i
\(73\) 13.1874 + 7.61374i 1.54347 + 0.891121i 0.998616 + 0.0525873i \(0.0167468\pi\)
0.544850 + 0.838533i \(0.316587\pi\)
\(74\) 8.73991i 1.01599i
\(75\) −0.423533 + 1.67947i −0.0489054 + 0.193929i
\(76\) −2.43077 1.40341i −0.278828 0.160982i
\(77\) −6.52125 9.76522i −0.743165 1.11285i
\(78\) −8.69628 + 2.46836i −0.984659 + 0.279487i
\(79\) −3.88551 + 6.72991i −0.437155 + 0.757174i −0.997469 0.0711063i \(-0.977347\pi\)
0.560314 + 0.828280i \(0.310680\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 4.95230 + 7.51497i 0.550255 + 0.834997i
\(82\) −5.02506 + 2.90122i −0.554925 + 0.320386i
\(83\) −2.84720 4.93150i −0.312521 0.541302i 0.666387 0.745606i \(-0.267840\pi\)
−0.978907 + 0.204304i \(0.934507\pi\)
\(84\) −2.97120 + 3.48884i −0.324185 + 0.380663i
\(85\) 3.46981 6.00989i 0.376354 0.651864i
\(86\) 2.05136i 0.221204i
\(87\) −3.49698 12.3202i −0.374916 1.32086i
\(88\) −4.43825 −0.473119
\(89\) 4.16961 + 7.22198i 0.441978 + 0.765528i 0.997836 0.0657488i \(-0.0209436\pi\)
−0.555858 + 0.831277i \(0.687610\pi\)
\(90\) 1.57607 + 2.55265i 0.166132 + 0.269073i
\(91\) −13.7792 + 0.899543i −1.44445 + 0.0942977i
\(92\) 3.01802 1.74245i 0.314650 0.181663i
\(93\) −0.994216 3.50272i −0.103095 0.363215i
\(94\) −8.95023 + 5.16742i −0.923145 + 0.532978i
\(95\) −2.43077 + 1.40341i −0.249392 + 0.143986i
\(96\) 0.472945 + 1.66623i 0.0482697 + 0.170059i
\(97\) −11.4765 + 6.62595i −1.16526 + 0.672763i −0.952559 0.304354i \(-0.901559\pi\)
−0.212701 + 0.977117i \(0.568226\pi\)
\(98\) −5.55569 + 4.25845i −0.561209 + 0.430168i
\(99\) −6.31395 + 11.7225i −0.634575 + 1.17815i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 18.1043 1.80144 0.900721 0.434399i \(-0.143039\pi\)
0.900721 + 0.434399i \(0.143039\pi\)
\(102\) −3.28206 11.5630i −0.324972 1.14491i
\(103\) 9.83724i 0.969292i −0.874710 0.484646i \(-0.838948\pi\)
0.874710 0.484646i \(-0.161052\pi\)
\(104\) −2.60957 + 4.51990i −0.255889 + 0.443213i
\(105\) 1.53582 + 4.31755i 0.149881 + 0.421350i
\(106\) 2.65743 + 4.60281i 0.258113 + 0.447064i
\(107\) 10.4663 6.04270i 1.01181 0.584170i 0.100090 0.994978i \(-0.468087\pi\)
0.911722 + 0.410809i \(0.134754\pi\)
\(108\) 5.07374 + 1.12125i 0.488220 + 0.107893i
\(109\) −1.65320 + 2.86343i −0.158348 + 0.274267i −0.934273 0.356558i \(-0.883950\pi\)
0.775925 + 0.630825i \(0.217283\pi\)
\(110\) −2.21912 + 3.84363i −0.211585 + 0.366476i
\(111\) −14.5627 + 4.13349i −1.38223 + 0.392334i
\(112\) 0.172355 + 2.64013i 0.0162860 + 0.249469i
\(113\) 2.79421 + 1.61324i 0.262857 + 0.151760i 0.625637 0.780114i \(-0.284839\pi\)
−0.362780 + 0.931875i \(0.618172\pi\)
\(114\) −1.18878 + 4.71395i −0.111339 + 0.441502i
\(115\) 3.48491i 0.324969i
\(116\) −6.40344 3.69703i −0.594545 0.343260i
\(117\) 8.22572 + 13.3226i 0.760468 + 1.23167i
\(118\) 1.06972i 0.0984758i
\(119\) −1.19608 18.3215i −0.109644 1.67953i
\(120\) 1.67947 + 0.423533i 0.153314 + 0.0386631i
\(121\) −8.69804 −0.790731
\(122\) −3.02264 5.23536i −0.273657 0.473987i
\(123\) 7.21067 + 7.00079i 0.650164 + 0.631240i
\(124\) −1.82054 1.05109i −0.163489 0.0943907i
\(125\) 1.00000 0.0894427
\(126\) 7.21842 + 3.30068i 0.643068 + 0.294048i
\(127\) 4.10553 0.364307 0.182154 0.983270i \(-0.441693\pi\)
0.182154 + 0.983270i \(0.441693\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 3.41805 0.970182i 0.300942 0.0854198i
\(130\) 2.60957 + 4.51990i 0.228874 + 0.396422i
\(131\) −19.4136 −1.69618 −0.848089 0.529854i \(-0.822247\pi\)
−0.848089 + 0.529854i \(0.822247\pi\)
\(132\) 2.09905 + 7.39514i 0.182699 + 0.643664i
\(133\) −3.28622 + 6.65943i −0.284951 + 0.577446i
\(134\) 4.92801i 0.425715i
\(135\) 3.50790 3.83336i 0.301912 0.329923i
\(136\) −6.00989 3.46981i −0.515343 0.297534i
\(137\) 9.19632i 0.785695i 0.919604 + 0.392847i \(0.128510\pi\)
−0.919604 + 0.392847i \(0.871490\pi\)
\(138\) −4.33068 4.20463i −0.368652 0.357922i
\(139\) −8.90078 5.13887i −0.754954 0.435873i 0.0725271 0.997366i \(-0.476894\pi\)
−0.827481 + 0.561494i \(0.810227\pi\)
\(140\) 2.37260 + 1.17080i 0.200521 + 0.0989508i
\(141\) 12.8431 + 12.4692i 1.08158 + 1.05010i
\(142\) 5.76938 9.99286i 0.484156 0.838582i
\(143\) −11.5819 + 20.0604i −0.968527 + 1.67754i
\(144\) 2.55265 1.57607i 0.212721 0.131339i
\(145\) −6.40344 + 3.69703i −0.531777 + 0.307021i
\(146\) −7.61374 13.1874i −0.630118 1.09140i
\(147\) 9.72308 + 7.24304i 0.801946 + 0.597396i
\(148\) −4.36995 + 7.56898i −0.359208 + 0.622166i
\(149\) 15.3288i 1.25578i 0.778302 + 0.627890i \(0.216081\pi\)
−0.778302 + 0.627890i \(0.783919\pi\)
\(150\) 1.20653 1.24270i 0.0985124 0.101466i
\(151\) 5.74675 0.467664 0.233832 0.972277i \(-0.424873\pi\)
0.233832 + 0.972277i \(0.424873\pi\)
\(152\) 1.40341 + 2.43077i 0.113831 + 0.197161i
\(153\) −17.7144 + 10.9373i −1.43212 + 0.884230i
\(154\) 0.764954 + 11.7176i 0.0616417 + 0.944228i
\(155\) −1.82054 + 1.05109i −0.146229 + 0.0844256i
\(156\) 8.76538 + 2.21047i 0.701792 + 0.176980i
\(157\) 6.17457 3.56489i 0.492784 0.284509i −0.232945 0.972490i \(-0.574836\pi\)
0.725729 + 0.687981i \(0.241503\pi\)
\(158\) 6.72991 3.88551i 0.535403 0.309115i
\(159\) 6.41252 6.60477i 0.508546 0.523792i
\(160\) 0.866025 0.500000i 0.0684653 0.0395285i
\(161\) −5.12047 7.66764i −0.403550 0.604295i
\(162\) −0.531331 8.98430i −0.0417453 0.705873i
\(163\) −1.11012 1.92279i −0.0869517 0.150605i 0.819270 0.573409i \(-0.194379\pi\)
−0.906221 + 0.422804i \(0.861046\pi\)
\(164\) 5.80244 0.453094
\(165\) 7.45390 + 1.87974i 0.580286 + 0.146338i
\(166\) 5.69440i 0.441971i
\(167\) 7.27271 12.5967i 0.562779 0.974762i −0.434473 0.900685i \(-0.643065\pi\)
0.997252 0.0740777i \(-0.0236013\pi\)
\(168\) 4.31755 1.53582i 0.333106 0.118491i
\(169\) 7.11967 + 12.3316i 0.547667 + 0.948587i
\(170\) −6.00989 + 3.46981i −0.460937 + 0.266122i
\(171\) 8.41676 0.248666i 0.643646 0.0190160i
\(172\) 1.02568 1.77653i 0.0782075 0.135459i
\(173\) −1.25357 + 2.17125i −0.0953073 + 0.165077i −0.909737 0.415185i \(-0.863717\pi\)
0.814430 + 0.580262i \(0.197050\pi\)
\(174\) −3.13163 + 12.4181i −0.237408 + 0.941414i
\(175\) 2.20024 1.46933i 0.166323 0.111071i
\(176\) 3.84363 + 2.21912i 0.289725 + 0.167273i
\(177\) 1.78240 0.505919i 0.133974 0.0380272i
\(178\) 8.33922i 0.625051i
\(179\) 6.45012 + 3.72398i 0.482105 + 0.278343i 0.721293 0.692630i \(-0.243548\pi\)
−0.239188 + 0.970973i \(0.576881\pi\)
\(180\) −0.0885938 2.99869i −0.00660339 0.223509i
\(181\) 6.18571i 0.459780i −0.973217 0.229890i \(-0.926163\pi\)
0.973217 0.229890i \(-0.0738367\pi\)
\(182\) 12.3829 + 6.11057i 0.917882 + 0.452946i
\(183\) −7.29377 + 7.51244i −0.539171 + 0.555336i
\(184\) −3.48491 −0.256911
\(185\) 4.36995 + 7.56898i 0.321285 + 0.556482i
\(186\) −0.890342 + 3.53055i −0.0652831 + 0.258872i
\(187\) −26.6734 15.3999i −1.95055 1.12615i
\(188\) 10.3348 0.753745
\(189\) 2.08577 13.5886i 0.151718 0.988424i
\(190\) 2.80681 0.203627
\(191\) −19.9088 11.4944i −1.44055 0.831704i −0.442667 0.896686i \(-0.645968\pi\)
−0.997886 + 0.0649822i \(0.979301\pi\)
\(192\) 0.423533 1.67947i 0.0305658 0.121205i
\(193\) 5.44323 + 9.42795i 0.391812 + 0.678638i 0.992689 0.120703i \(-0.0385150\pi\)
−0.600877 + 0.799342i \(0.705182\pi\)
\(194\) 13.2519 0.951431
\(195\) 6.29702 6.48580i 0.450939 0.464458i
\(196\) 6.94059 0.910079i 0.495756 0.0650057i
\(197\) 7.07434i 0.504026i 0.967724 + 0.252013i \(0.0810926\pi\)
−0.967724 + 0.252013i \(0.918907\pi\)
\(198\) 11.3293 6.99499i 0.805137 0.497112i
\(199\) 15.9968 + 9.23577i 1.13398 + 0.654706i 0.944934 0.327261i \(-0.106126\pi\)
0.189051 + 0.981967i \(0.439459\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 8.21120 2.33068i 0.579173 0.164393i
\(202\) −15.6788 9.05213i −1.10315 0.636906i
\(203\) −8.65698 + 17.5431i −0.607601 + 1.23129i
\(204\) −2.93916 + 11.6549i −0.205782 + 0.816005i
\(205\) 2.90122 5.02506i 0.202630 0.350965i
\(206\) −4.91862 + 8.51930i −0.342697 + 0.593568i
\(207\) −4.95770 + 9.20447i −0.344584 + 0.639755i
\(208\) 4.51990 2.60957i 0.313399 0.180941i
\(209\) 6.22866 + 10.7884i 0.430845 + 0.746246i
\(210\) 0.828717 4.50702i 0.0571869 0.311014i
\(211\) −3.88575 + 6.73032i −0.267506 + 0.463334i −0.968217 0.250111i \(-0.919533\pi\)
0.700711 + 0.713445i \(0.252866\pi\)
\(212\) 5.31487i 0.365027i
\(213\) −19.3790 4.88704i −1.32783 0.334855i
\(214\) −12.0854 −0.826141
\(215\) −1.02568 1.77653i −0.0699509 0.121159i
\(216\) −3.83336 3.50790i −0.260827 0.238682i
\(217\) −2.46124 + 4.98763i −0.167080 + 0.338582i
\(218\) 2.86343 1.65320i 0.193936 0.111969i
\(219\) −18.3723 + 18.9231i −1.24149 + 1.27871i
\(220\) 3.84363 2.21912i 0.259138 0.149613i
\(221\) −31.3664 + 18.1094i −2.10993 + 1.21817i
\(222\) 14.6784 + 3.70164i 0.985150 + 0.248438i
\(223\) 1.25245 0.723100i 0.0838699 0.0484223i −0.457479 0.889221i \(-0.651247\pi\)
0.541348 + 0.840798i \(0.317914\pi\)
\(224\) 1.17080 2.37260i 0.0782275 0.158526i
\(225\) −2.64124 1.42262i −0.176083 0.0948414i
\(226\) −1.61324 2.79421i −0.107311 0.185868i
\(227\) −8.46455 −0.561812 −0.280906 0.959735i \(-0.590635\pi\)
−0.280906 + 0.959735i \(0.590635\pi\)
\(228\) 3.38649 3.48802i 0.224276 0.230999i
\(229\) 13.7837i 0.910853i −0.890273 0.455427i \(-0.849487\pi\)
0.890273 0.455427i \(-0.150513\pi\)
\(230\) −1.74245 + 3.01802i −0.114894 + 0.199002i
\(231\) 19.1624 6.81635i 1.26079 0.448483i
\(232\) 3.69703 + 6.40344i 0.242722 + 0.420406i
\(233\) 16.7359 9.66250i 1.09641 0.633011i 0.161133 0.986933i \(-0.448485\pi\)
0.935275 + 0.353921i \(0.115152\pi\)
\(234\) −0.462383 15.6506i −0.0302269 1.02311i
\(235\) 5.16742 8.95023i 0.337085 0.583848i
\(236\) 0.534861 0.926406i 0.0348165 0.0603039i
\(237\) −9.65704 9.37594i −0.627292 0.609033i
\(238\) −8.12492 + 16.4649i −0.526660 + 1.06726i
\(239\) −7.14170 4.12327i −0.461958 0.266712i 0.250909 0.968011i \(-0.419271\pi\)
−0.712867 + 0.701299i \(0.752604\pi\)
\(240\) −1.24270 1.20653i −0.0802158 0.0778809i
\(241\) 23.9106i 1.54022i −0.637914 0.770108i \(-0.720203\pi\)
0.637914 0.770108i \(-0.279797\pi\)
\(242\) 7.53272 + 4.34902i 0.484222 + 0.279566i
\(243\) −14.7186 + 5.13440i −0.944200 + 0.329372i
\(244\) 6.04527i 0.387009i
\(245\) 2.68214 6.46576i 0.171356 0.413083i
\(246\) −2.74423 9.66820i −0.174966 0.616422i
\(247\) 14.6491 0.932101
\(248\) 1.05109 + 1.82054i 0.0667443 + 0.115605i
\(249\) 9.48818 2.69314i 0.601289 0.170671i
\(250\) −0.866025 0.500000i −0.0547723 0.0316228i
\(251\) −21.8070 −1.37644 −0.688222 0.725500i \(-0.741609\pi\)
−0.688222 + 0.725500i \(0.741609\pi\)
\(252\) −4.60099 6.46768i −0.289835 0.407425i
\(253\) −15.4669 −0.972394
\(254\) −3.55550 2.05277i −0.223092 0.128802i
\(255\) 8.62385 + 8.37283i 0.540046 + 0.524327i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.0751 −0.628471 −0.314235 0.949345i \(-0.601748\pi\)
−0.314235 + 0.949345i \(0.601748\pi\)
\(258\) −3.44521 0.868820i −0.214489 0.0540904i
\(259\) 20.7363 + 10.2327i 1.28849 + 0.635829i
\(260\) 5.21913i 0.323677i
\(261\) 22.1725 0.655068i 1.37244 0.0405477i
\(262\) 16.8127 + 9.70682i 1.03869 + 0.599690i
\(263\) 1.97563i 0.121823i −0.998143 0.0609113i \(-0.980599\pi\)
0.998143 0.0609113i \(-0.0194007\pi\)
\(264\) 1.87974 7.45390i 0.115690 0.458756i
\(265\) −4.60281 2.65743i −0.282748 0.163245i
\(266\) 6.17567 4.12413i 0.378654 0.252867i
\(267\) −13.8951 + 3.94399i −0.850364 + 0.241368i
\(268\) 2.46400 4.26778i 0.150513 0.260696i
\(269\) 4.12540 7.14541i 0.251530 0.435663i −0.712417 0.701756i \(-0.752400\pi\)
0.963947 + 0.266093i \(0.0857329\pi\)
\(270\) −4.95461 + 1.56583i −0.301528 + 0.0952936i
\(271\) 24.8880 14.3691i 1.51184 0.872859i 0.511932 0.859026i \(-0.328930\pi\)
0.999904 0.0138328i \(-0.00440326\pi\)
\(272\) 3.46981 + 6.00989i 0.210388 + 0.364403i
\(273\) 4.32519 23.5227i 0.261772 1.42366i
\(274\) 4.59816 7.96425i 0.277785 0.481138i
\(275\) 4.43825i 0.267636i
\(276\) 1.64817 + 5.80665i 0.0992081 + 0.349520i
\(277\) 20.4226 1.22707 0.613537 0.789666i \(-0.289746\pi\)
0.613537 + 0.789666i \(0.289746\pi\)
\(278\) 5.13887 + 8.90078i 0.308209 + 0.533833i
\(279\) 6.30379 0.186240i 0.377398 0.0111499i
\(280\) −1.46933 2.20024i −0.0878092 0.131490i
\(281\) −1.53417 + 0.885754i −0.0915209 + 0.0528396i −0.545062 0.838396i \(-0.683494\pi\)
0.453541 + 0.891235i \(0.350161\pi\)
\(282\) −4.88781 17.2202i −0.291065 1.02545i
\(283\) 2.09766 1.21108i 0.124693 0.0719915i −0.436356 0.899774i \(-0.643731\pi\)
0.561049 + 0.827783i \(0.310398\pi\)
\(284\) −9.99286 + 5.76938i −0.592967 + 0.342350i
\(285\) −1.32747 4.67679i −0.0786323 0.277029i
\(286\) 20.0604 11.5819i 1.18620 0.684852i
\(287\) −1.00008 15.3192i −0.0590328 0.904263i
\(288\) −2.99869 + 0.0885938i −0.176700 + 0.00522044i
\(289\) −15.5792 26.9839i −0.916421 1.58729i
\(290\) 7.39406 0.434194
\(291\) −6.26742 22.0807i −0.367403 1.29439i
\(292\) 15.2275i 0.891121i
\(293\) −5.58519 + 9.67384i −0.326290 + 0.565152i −0.981773 0.190059i \(-0.939132\pi\)
0.655482 + 0.755211i \(0.272465\pi\)
\(294\) −4.79892 11.1342i −0.279879 0.649360i
\(295\) −0.534861 0.926406i −0.0311408 0.0539374i
\(296\) 7.56898 4.36995i 0.439938 0.253998i
\(297\) −17.0134 15.5689i −0.987217 0.903401i
\(298\) 7.66438 13.2751i 0.443985 0.769005i
\(299\) −9.09409 + 15.7514i −0.525925 + 0.910929i
\(300\) −1.66623 + 0.472945i −0.0961998 + 0.0273055i
\(301\) −4.86706 2.40174i −0.280533 0.138434i
\(302\) −4.97683 2.87338i −0.286384 0.165344i
\(303\) −7.66775 + 30.4056i −0.440501 + 1.74675i
\(304\) 2.80681i 0.160982i
\(305\) 5.23536 + 3.02264i 0.299776 + 0.173076i
\(306\) 20.8098 0.614807i 1.18962 0.0351462i
\(307\) 2.48600i 0.141884i 0.997480 + 0.0709419i \(0.0226005\pi\)
−0.997480 + 0.0709419i \(0.977400\pi\)
\(308\) 5.19631 10.5302i 0.296087 0.600013i
\(309\) 16.5214 + 4.16640i 0.939867 + 0.237018i
\(310\) 2.10218 0.119396
\(311\) −3.31033 5.73365i −0.187711 0.325126i 0.756775 0.653675i \(-0.226774\pi\)
−0.944487 + 0.328549i \(0.893440\pi\)
\(312\) −6.48580 6.29702i −0.367186 0.356498i
\(313\) −22.1815 12.8065i −1.25377 0.723866i −0.281916 0.959439i \(-0.590970\pi\)
−0.971857 + 0.235573i \(0.924303\pi\)
\(314\) −7.12978 −0.402357
\(315\) −7.90167 + 0.750738i −0.445209 + 0.0422993i
\(316\) −7.77103 −0.437155
\(317\) −16.9737 9.79975i −0.953336 0.550409i −0.0592204 0.998245i \(-0.518861\pi\)
−0.894116 + 0.447836i \(0.852195\pi\)
\(318\) −8.85579 + 2.51364i −0.496608 + 0.140958i
\(319\) 16.4083 + 28.4201i 0.918690 + 1.59122i
\(320\) −1.00000 −0.0559017
\(321\) 5.71573 + 20.1371i 0.319021 + 1.12394i
\(322\) 0.600641 + 9.20061i 0.0334724 + 0.512730i
\(323\) 19.4782i 1.08380i
\(324\) −4.03201 + 8.04630i −0.224000 + 0.447017i
\(325\) −4.51990 2.60957i −0.250719 0.144753i
\(326\) 2.22025i 0.122968i
\(327\) −4.10886 3.98926i −0.227220 0.220606i
\(328\) −5.02506 2.90122i −0.277462 0.160193i
\(329\) −1.78126 27.2853i −0.0982040 1.50429i
\(330\) −5.51540 5.35486i −0.303613 0.294775i
\(331\) 11.3343 19.6316i 0.622991 1.07905i −0.365934 0.930641i \(-0.619251\pi\)
0.988926 0.148412i \(-0.0474161\pi\)
\(332\) 2.84720 4.93150i 0.156260 0.270651i
\(333\) −0.774301 26.2083i −0.0424315 1.43620i
\(334\) −12.5967 + 7.27271i −0.689261 + 0.397945i
\(335\) −2.46400 4.26778i −0.134623 0.233174i
\(336\) −4.50702 0.828717i −0.245878 0.0452102i
\(337\) −9.56790 + 16.5721i −0.521196 + 0.902739i 0.478500 + 0.878088i \(0.341181\pi\)
−0.999696 + 0.0246511i \(0.992153\pi\)
\(338\) 14.2393i 0.774518i
\(339\) −3.89282 + 4.00953i −0.211429 + 0.217768i
\(340\) 6.93962 0.376354
\(341\) 4.66500 + 8.08001i 0.252624 + 0.437557i
\(342\) −7.41346 3.99303i −0.400874 0.215918i
\(343\) −3.59897 18.1672i −0.194326 0.980937i
\(344\) −1.77653 + 1.02568i −0.0957843 + 0.0553011i
\(345\) 5.85279 + 1.47597i 0.315104 + 0.0794636i
\(346\) 2.17125 1.25357i 0.116727 0.0673924i
\(347\) 0.443672 0.256154i 0.0238176 0.0137511i −0.488044 0.872819i \(-0.662289\pi\)
0.511862 + 0.859068i \(0.328956\pi\)
\(348\) 8.92112 9.18858i 0.478222 0.492559i
\(349\) −1.14174 + 0.659186i −0.0611161 + 0.0352854i −0.530247 0.847843i \(-0.677901\pi\)
0.469131 + 0.883129i \(0.344567\pi\)
\(350\) −2.64013 + 0.172355i −0.141121 + 0.00921276i
\(351\) −25.8588 + 8.17229i −1.38024 + 0.436205i
\(352\) −2.21912 3.84363i −0.118280 0.204866i
\(353\) 12.3002 0.654672 0.327336 0.944908i \(-0.393849\pi\)
0.327336 + 0.944908i \(0.393849\pi\)
\(354\) −1.79656 0.453062i −0.0954864 0.0240800i
\(355\) 11.5388i 0.612414i
\(356\) −4.16961 + 7.22198i −0.220989 + 0.382764i
\(357\) 31.2770 + 5.75098i 1.65535 + 0.304374i
\(358\) −3.72398 6.45012i −0.196819 0.340900i
\(359\) 20.6370 11.9148i 1.08918 0.628837i 0.155820 0.987785i \(-0.450198\pi\)
0.933357 + 0.358948i \(0.116865\pi\)
\(360\) −1.42262 + 2.64124i −0.0749787 + 0.139206i
\(361\) −5.56091 + 9.63178i −0.292679 + 0.506936i
\(362\) −3.09285 + 5.35698i −0.162557 + 0.281557i
\(363\) 3.68390 14.6081i 0.193355 0.766726i
\(364\) −7.66863 11.4834i −0.401945 0.601892i
\(365\) 13.1874 + 7.61374i 0.690259 + 0.398521i
\(366\) 10.0728 2.85908i 0.526514 0.149447i
\(367\) 30.1194i 1.57222i 0.618087 + 0.786110i \(0.287908\pi\)
−0.618087 + 0.786110i \(0.712092\pi\)
\(368\) 3.01802 + 1.74245i 0.157325 + 0.0908316i
\(369\) −14.8116 + 9.14505i −0.771059 + 0.476072i
\(370\) 8.73991i 0.454366i
\(371\) −14.0319 + 0.916043i −0.728502 + 0.0475586i
\(372\) 2.53633 2.61237i 0.131503 0.135445i
\(373\) 36.8547 1.90826 0.954131 0.299389i \(-0.0967829\pi\)
0.954131 + 0.299389i \(0.0967829\pi\)
\(374\) 15.3999 + 26.6734i 0.796308 + 1.37925i
\(375\) −0.423533 + 1.67947i −0.0218711 + 0.0867275i
\(376\) −8.95023 5.16742i −0.461573 0.266489i
\(377\) 38.5906 1.98752
\(378\) −8.60062 + 10.7252i −0.442368 + 0.551643i
\(379\) −3.10706 −0.159599 −0.0797994 0.996811i \(-0.525428\pi\)
−0.0797994 + 0.996811i \(0.525428\pi\)
\(380\) −2.43077 1.40341i −0.124696 0.0719932i
\(381\) −1.73883 + 6.89512i −0.0890828 + 0.353248i
\(382\) 11.4944 + 19.9088i 0.588103 + 1.01863i
\(383\) −11.1938 −0.571979 −0.285990 0.958233i \(-0.592322\pi\)
−0.285990 + 0.958233i \(0.592322\pi\)
\(384\) −1.20653 + 1.24270i −0.0615702 + 0.0634161i
\(385\) −6.52125 9.76522i −0.332354 0.497682i
\(386\) 10.8865i 0.554106i
\(387\) 0.181738 + 6.15141i 0.00923827 + 0.312694i
\(388\) −11.4765 6.62595i −0.582630 0.336382i
\(389\) 22.9992i 1.16610i 0.812435 + 0.583052i \(0.198142\pi\)
−0.812435 + 0.583052i \(0.801858\pi\)
\(390\) −8.69628 + 2.46836i −0.440353 + 0.124990i
\(391\) −20.9439 12.0920i −1.05918 0.611517i
\(392\) −6.46576 2.68214i −0.326570 0.135469i
\(393\) 8.22232 32.6046i 0.414761 1.64469i
\(394\) 3.53717 6.12656i 0.178200 0.308652i
\(395\) −3.88551 + 6.72991i −0.195501 + 0.338618i
\(396\) −13.3089 + 0.393201i −0.668799 + 0.0197591i
\(397\) −6.76832 + 3.90769i −0.339692 + 0.196121i −0.660136 0.751146i \(-0.729501\pi\)
0.320444 + 0.947268i \(0.396168\pi\)
\(398\) −9.23577 15.9968i −0.462947 0.801848i
\(399\) −9.79250 8.33959i −0.490238 0.417502i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 11.6348i 0.581015i 0.956873 + 0.290507i \(0.0938241\pi\)
−0.956873 + 0.290507i \(0.906176\pi\)
\(402\) −8.27644 2.08717i −0.412791 0.104099i
\(403\) 10.9716 0.546532
\(404\) 9.05213 + 15.6788i 0.450360 + 0.780047i
\(405\) 4.95230 + 7.51497i 0.246082 + 0.373422i
\(406\) 16.2687 10.8643i 0.807403 0.539186i
\(407\) 33.5930 19.3949i 1.66514 0.961371i
\(408\) 8.37283 8.62385i 0.414517 0.426944i
\(409\) 24.2276 13.9878i 1.19798 0.691653i 0.237874 0.971296i \(-0.423549\pi\)
0.960104 + 0.279643i \(0.0902161\pi\)
\(410\) −5.02506 + 2.90122i −0.248170 + 0.143281i
\(411\) −15.4450 3.89494i −0.761843 0.192123i
\(412\) 8.51930 4.91862i 0.419716 0.242323i
\(413\) −2.53802 1.25243i −0.124888 0.0616281i
\(414\) 8.89573 5.49246i 0.437201 0.269939i
\(415\) −2.84720 4.93150i −0.139764 0.242078i
\(416\) −5.21913 −0.255889
\(417\) 12.4003 12.7721i 0.607247 0.625453i
\(418\) 12.4573i 0.609307i
\(419\) 1.60593 2.78155i 0.0784549 0.135888i −0.824129 0.566403i \(-0.808335\pi\)
0.902583 + 0.430515i \(0.141668\pi\)
\(420\) −2.97120 + 3.48884i −0.144980 + 0.170238i
\(421\) 3.72961 + 6.45987i 0.181770 + 0.314835i 0.942483 0.334253i \(-0.108484\pi\)
−0.760713 + 0.649088i \(0.775151\pi\)
\(422\) 6.73032 3.88575i 0.327627 0.189155i
\(423\) −26.3812 + 16.2884i −1.28270 + 0.791970i
\(424\) −2.65743 + 4.60281i −0.129056 + 0.223532i
\(425\) 3.46981 6.00989i 0.168310 0.291522i
\(426\) 14.3392 + 13.9218i 0.694736 + 0.674514i
\(427\) 15.9603 1.04193i 0.772374 0.0504226i
\(428\) 10.4663 + 6.04270i 0.505906 + 0.292085i
\(429\) −28.7856 27.9477i −1.38978 1.34933i
\(430\) 2.05136i 0.0989256i
\(431\) −12.2228 7.05686i −0.588753 0.339917i 0.175851 0.984417i \(-0.443732\pi\)
−0.764604 + 0.644500i \(0.777066\pi\)
\(432\) 1.56583 + 4.95461i 0.0753362 + 0.238379i
\(433\) 17.9235i 0.861348i 0.902508 + 0.430674i \(0.141724\pi\)
−0.902508 + 0.430674i \(0.858276\pi\)
\(434\) 4.62531 3.08880i 0.222022 0.148267i
\(435\) −3.49698 12.3202i −0.167667 0.590708i
\(436\) −3.30640 −0.158348
\(437\) 4.89073 + 8.47100i 0.233956 + 0.405223i
\(438\) 25.3725 7.20176i 1.21234 0.344113i
\(439\) 33.6745 + 19.4420i 1.60719 + 0.927914i 0.989994 + 0.141109i \(0.0450667\pi\)
0.617201 + 0.786806i \(0.288267\pi\)
\(440\) −4.43825 −0.211585
\(441\) −16.2825 + 13.2620i −0.775358 + 0.631522i
\(442\) 36.2188 1.72275
\(443\) 23.5754 + 13.6113i 1.12010 + 0.646692i 0.941427 0.337216i \(-0.109485\pi\)
0.178676 + 0.983908i \(0.442819\pi\)
\(444\) −10.8611 10.5449i −0.515443 0.500440i
\(445\) 4.16961 + 7.22198i 0.197659 + 0.342355i
\(446\) −1.44620 −0.0684795
\(447\) −25.7442 6.49223i −1.21766 0.307072i
\(448\) −2.20024 + 1.46933i −0.103952 + 0.0694193i
\(449\) 16.5846i 0.782674i −0.920248 0.391337i \(-0.872013\pi\)
0.920248 0.391337i \(-0.127987\pi\)
\(450\) 1.57607 + 2.55265i 0.0742967 + 0.120333i
\(451\) −22.3024 12.8763i −1.05018 0.606322i
\(452\) 3.22647i 0.151760i
\(453\) −2.43394 + 9.65150i −0.114356 + 0.453467i
\(454\) 7.33052 + 4.23228i 0.344038 + 0.198631i
\(455\) −13.7792 + 0.899543i −0.645979 + 0.0421712i
\(456\) −4.67679 + 1.32747i −0.219011 + 0.0621643i
\(457\) −8.76829 + 15.1871i −0.410163 + 0.710424i −0.994907 0.100794i \(-0.967862\pi\)
0.584744 + 0.811218i \(0.301195\pi\)
\(458\) −6.89186 + 11.9370i −0.322035 + 0.557782i
\(459\) −10.8663 34.3831i −0.507195 1.60487i
\(460\) 3.01802 1.74245i 0.140716 0.0812423i
\(461\) 17.8733 + 30.9575i 0.832444 + 1.44184i 0.896095 + 0.443863i \(0.146392\pi\)
−0.0636506 + 0.997972i \(0.520274\pi\)
\(462\) −20.0033 3.67805i −0.930636 0.171118i
\(463\) 10.2703 17.7886i 0.477299 0.826707i −0.522362 0.852724i \(-0.674949\pi\)
0.999661 + 0.0260170i \(0.00828242\pi\)
\(464\) 7.39406i 0.343260i
\(465\) −0.994216 3.50272i −0.0461056 0.162435i
\(466\) −19.3250 −0.895213
\(467\) 3.54772 + 6.14483i 0.164169 + 0.284349i 0.936360 0.351042i \(-0.114173\pi\)
−0.772191 + 0.635390i \(0.780839\pi\)
\(468\) −7.42485 + 13.7850i −0.343214 + 0.637211i
\(469\) −11.6922 5.76972i −0.539895 0.266421i
\(470\) −8.95023 + 5.16742i −0.412843 + 0.238355i
\(471\) 3.37199 + 11.8799i 0.155373 + 0.547395i
\(472\) −0.926406 + 0.534861i −0.0426413 + 0.0246190i
\(473\) −7.88470 + 4.55223i −0.362539 + 0.209312i
\(474\) 3.67527 + 12.9483i 0.168811 + 0.594736i
\(475\) −2.43077 + 1.40341i −0.111531 + 0.0643926i
\(476\) 15.2689 10.1966i 0.699847 0.467360i
\(477\) 8.37660 + 13.5670i 0.383538 + 0.621189i
\(478\) 4.12327 + 7.14170i 0.188594 + 0.326654i
\(479\) 17.3106 0.790942 0.395471 0.918478i \(-0.370581\pi\)
0.395471 + 0.918478i \(0.370581\pi\)
\(480\) 0.472945 + 1.66623i 0.0215869 + 0.0760527i
\(481\) 45.6147i 2.07985i
\(482\) −11.9553 + 20.7072i −0.544548 + 0.943185i
\(483\) 15.0463 5.35219i 0.684629 0.243533i
\(484\) −4.34902 7.53272i −0.197683 0.342396i
\(485\) −11.4765 + 6.62595i −0.521120 + 0.300869i
\(486\) 15.3139 + 2.91279i 0.694653 + 0.132127i
\(487\) −17.8900 + 30.9864i −0.810675 + 1.40413i 0.101718 + 0.994813i \(0.467566\pi\)
−0.912393 + 0.409316i \(0.865767\pi\)
\(488\) 3.02264 5.23536i 0.136828 0.236994i
\(489\) 3.69945 1.05006i 0.167295 0.0474852i
\(490\) −5.55569 + 4.25845i −0.250980 + 0.192377i
\(491\) 24.0944 + 13.9109i 1.08736 + 0.627789i 0.932873 0.360205i \(-0.117293\pi\)
0.154490 + 0.987994i \(0.450627\pi\)
\(492\) −2.45752 + 9.74502i −0.110794 + 0.439339i
\(493\) 51.3119i 2.31097i
\(494\) −12.6865 7.32456i −0.570793 0.329547i
\(495\) −6.31395 + 11.7225i −0.283791 + 0.526886i
\(496\) 2.10218i 0.0943907i
\(497\) 16.9542 + 25.3881i 0.760502 + 1.13881i
\(498\) −9.56358 2.41177i −0.428554 0.108074i
\(499\) −10.7082 −0.479365 −0.239683 0.970851i \(-0.577043\pi\)
−0.239683 + 0.970851i \(0.577043\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 18.0756 + 17.5494i 0.807557 + 0.784050i
\(502\) 18.8854 + 10.9035i 0.842897 + 0.486647i
\(503\) 26.8197 1.19583 0.597916 0.801559i \(-0.295996\pi\)
0.597916 + 0.801559i \(0.295996\pi\)
\(504\) 0.750738 + 7.90167i 0.0334406 + 0.351968i
\(505\) 18.1043 0.805629
\(506\) 13.3947 + 7.73344i 0.595467 + 0.343793i
\(507\) −23.7260 + 6.73443i −1.05371 + 0.299086i
\(508\) 2.05277 + 3.55550i 0.0910768 + 0.157750i
\(509\) −10.7357 −0.475852 −0.237926 0.971283i \(-0.576468\pi\)
−0.237926 + 0.971283i \(0.576468\pi\)
\(510\) −3.28206 11.5630i −0.145332 0.512018i
\(511\) 40.2025 2.62453i 1.77846 0.116102i
\(512\) 1.00000i 0.0441942i
\(513\) −3.14715 + 14.2410i −0.138950 + 0.628756i
\(514\) 8.72534 + 5.03757i 0.384858 + 0.222198i
\(515\) 9.83724i 0.433481i
\(516\) 2.54923 + 2.47502i 0.112223 + 0.108957i
\(517\) −39.7233 22.9343i −1.74703 1.00865i
\(518\) −12.8418 19.2299i −0.564236 0.844914i
\(519\) −3.11562 3.02493i −0.136761 0.132780i
\(520\) −2.60957 + 4.51990i −0.114437 + 0.198211i
\(521\) −3.27417 + 5.67102i −0.143444 + 0.248452i −0.928791 0.370603i \(-0.879151\pi\)
0.785347 + 0.619055i \(0.212484\pi\)
\(522\) −19.5295 10.5189i −0.854782 0.460402i
\(523\) 27.2374 15.7255i 1.19101 0.687628i 0.232472 0.972603i \(-0.425319\pi\)
0.958535 + 0.284975i \(0.0919853\pi\)
\(524\) −9.70682 16.8127i −0.424045 0.734467i
\(525\) 1.53582 + 4.31755i 0.0670287 + 0.188433i
\(526\) −0.987816 + 1.71095i −0.0430708 + 0.0746008i
\(527\) 14.5883i 0.635478i
\(528\) −5.35486 + 5.51540i −0.233040 + 0.240027i
\(529\) 10.8554 0.471975
\(530\) 2.65743 + 4.60281i 0.115432 + 0.199933i
\(531\) 0.0947707 + 3.20776i 0.00411270 + 0.139205i
\(532\) −7.41035 + 0.483768i −0.321279 + 0.0209740i
\(533\) −26.2264 + 15.1418i −1.13599 + 0.655866i
\(534\) 14.0055 + 3.53193i 0.606076 + 0.152842i
\(535\) 10.4663 6.04270i 0.452496 0.261249i
\(536\) −4.26778 + 2.46400i −0.184340 + 0.106429i
\(537\) −8.98615 + 9.25556i −0.387781 + 0.399407i
\(538\) −7.14541 + 4.12540i −0.308060 + 0.177859i
\(539\) −28.6967 11.9040i −1.23605 0.512742i
\(540\) 5.07374 + 1.12125i 0.218339 + 0.0482511i
\(541\) 3.61196 + 6.25610i 0.155290 + 0.268971i 0.933165 0.359449i \(-0.117035\pi\)
−0.777874 + 0.628420i \(0.783702\pi\)
\(542\) −28.7381 −1.23441
\(543\) 10.3887 + 2.61985i 0.445822 + 0.112429i
\(544\) 6.93962i 0.297534i
\(545\) −1.65320 + 2.86343i −0.0708153 + 0.122656i
\(546\) −15.5071 + 18.2087i −0.663642 + 0.779260i
\(547\) −3.09371 5.35846i −0.132277 0.229111i 0.792277 0.610162i \(-0.208896\pi\)
−0.924554 + 0.381051i \(0.875562\pi\)
\(548\) −7.96425 + 4.59816i −0.340216 + 0.196424i
\(549\) −9.52777 15.4314i −0.406635 0.658598i
\(550\) −2.21912 + 3.84363i −0.0946237 + 0.163893i
\(551\) 10.3769 17.9732i 0.442069 0.765686i
\(552\) 1.47597 5.85279i 0.0628215 0.249111i
\(553\) 1.33937 + 20.5165i 0.0569560 + 0.872452i
\(554\) −17.6865 10.2113i −0.751427 0.433837i
\(555\) −14.5627 + 4.13349i −0.618152 + 0.175457i
\(556\) 10.2777i 0.435873i
\(557\) 3.23352 + 1.86687i 0.137009 + 0.0791020i 0.566938 0.823761i \(-0.308128\pi\)
−0.429929 + 0.902863i \(0.641461\pi\)
\(558\) −5.55236 2.99061i −0.235050 0.126602i
\(559\) 10.7063i 0.452830i
\(560\) 0.172355 + 2.64013i 0.00728332 + 0.111566i
\(561\) 37.1607 38.2748i 1.56892 1.61596i
\(562\) 1.77151 0.0747265
\(563\) −2.05579 3.56073i −0.0866411 0.150067i 0.819448 0.573153i \(-0.194280\pi\)
−0.906089 + 0.423086i \(0.860947\pi\)
\(564\) −4.37714 + 17.3570i −0.184311 + 0.730863i
\(565\) 2.79421 + 1.61324i 0.117553 + 0.0678693i
\(566\) −2.42217 −0.101811
\(567\) 21.9382 + 9.25820i 0.921319 + 0.388808i
\(568\) 11.5388 0.484156
\(569\) −17.0126 9.82222i −0.713205 0.411769i 0.0990419 0.995083i \(-0.468422\pi\)
−0.812246 + 0.583314i \(0.801756\pi\)
\(570\) −1.18878 + 4.71395i −0.0497924 + 0.197446i
\(571\) 21.3658 + 37.0067i 0.894132 + 1.54868i 0.834875 + 0.550440i \(0.185540\pi\)
0.0592571 + 0.998243i \(0.481127\pi\)
\(572\) −23.1638 −0.968527
\(573\) 27.7365 28.5681i 1.15871 1.19345i
\(574\) −6.79350 + 13.7669i −0.283555 + 0.574617i
\(575\) 3.48491i 0.145331i
\(576\) 2.64124 + 1.42262i 0.110052 + 0.0592759i
\(577\) −18.1866 10.5000i −0.757117 0.437122i 0.0711425 0.997466i \(-0.477335\pi\)
−0.828260 + 0.560344i \(0.810669\pi\)
\(578\) 31.1583i 1.29601i
\(579\) −18.1393 + 5.14869i −0.753845 + 0.213972i
\(580\) −6.40344 3.69703i −0.265888 0.153511i
\(581\) −13.5105 6.66702i −0.560511 0.276594i
\(582\) −5.61261 + 22.2562i −0.232650 + 0.922548i
\(583\) −11.7943 + 20.4284i −0.488472 + 0.846058i
\(584\) 7.61374 13.1874i 0.315059 0.545698i
\(585\) 8.22572 + 13.3226i 0.340092 + 0.550822i
\(586\) 9.67384 5.58519i 0.399623 0.230722i
\(587\) −0.432150 0.748507i −0.0178368 0.0308942i 0.856969 0.515368i \(-0.172345\pi\)
−0.874806 + 0.484473i \(0.839011\pi\)
\(588\) −1.41112 + 12.0420i −0.0581934 + 0.496602i
\(589\) 2.95021 5.10991i 0.121561 0.210550i
\(590\) 1.06972i 0.0440397i
\(591\) −11.8812 2.99622i −0.488725 0.123248i
\(592\) −8.73991 −0.359208
\(593\) −0.642454 1.11276i −0.0263824 0.0456957i 0.852533 0.522674i \(-0.175065\pi\)
−0.878915 + 0.476978i \(0.841732\pi\)
\(594\) 6.94956 + 21.9898i 0.285144 + 0.902252i
\(595\) −1.19608 18.3215i −0.0490344 0.751109i
\(596\) −13.2751 + 7.66438i −0.543769 + 0.313945i
\(597\) −22.2864 + 22.9545i −0.912121 + 0.939467i
\(598\) 15.7514 9.09409i 0.644124 0.371885i
\(599\) −0.953971 + 0.550775i −0.0389782 + 0.0225041i −0.519362 0.854554i \(-0.673831\pi\)
0.480384 + 0.877058i \(0.340497\pi\)
\(600\) 1.67947 + 0.423533i 0.0685641 + 0.0172907i
\(601\) 0.162569 0.0938594i 0.00663134 0.00382860i −0.496681 0.867933i \(-0.665448\pi\)
0.503312 + 0.864105i \(0.332115\pi\)
\(602\) 3.01413 + 4.51350i 0.122847 + 0.183957i
\(603\) 0.436591 + 14.7776i 0.0177794 + 0.601789i
\(604\) 2.87338 + 4.97683i 0.116916 + 0.202504i
\(605\) −8.69804 −0.353626
\(606\) 21.8432 22.4981i 0.887321 0.913924i
\(607\) 2.78981i 0.113235i 0.998396 + 0.0566175i \(0.0180315\pi\)
−0.998396 + 0.0566175i \(0.981968\pi\)
\(608\) −1.40341 + 2.43077i −0.0569156 + 0.0985807i
\(609\) −25.7966 21.9692i −1.04533 0.890238i
\(610\) −3.02264 5.23536i −0.122383 0.211973i
\(611\) −46.7124 + 26.9694i −1.88978 + 1.09107i
\(612\) −18.3292 9.87245i −0.740914 0.399070i
\(613\) 15.0929 26.1417i 0.609598 1.05586i −0.381708 0.924283i \(-0.624664\pi\)
0.991307 0.131572i \(-0.0420026\pi\)
\(614\) 1.24300 2.15294i 0.0501635 0.0868857i
\(615\) 7.21067 + 7.00079i 0.290762 + 0.282299i
\(616\) −9.76522 + 6.52125i −0.393452 + 0.262749i
\(617\) 18.6357 + 10.7593i 0.750246 + 0.433155i 0.825783 0.563988i \(-0.190734\pi\)
−0.0755367 + 0.997143i \(0.524067\pi\)
\(618\) −12.2247 11.8689i −0.491750 0.477437i
\(619\) 26.6566i 1.07142i −0.844402 0.535710i \(-0.820044\pi\)
0.844402 0.535710i \(-0.179956\pi\)
\(620\) −1.82054 1.05109i −0.0731147 0.0422128i
\(621\) −13.3589 12.2247i −0.536074 0.490561i
\(622\) 6.62065i 0.265464i
\(623\) 19.7856 + 9.76358i 0.792694 + 0.391170i
\(624\) 2.46836 + 8.69628i 0.0988136 + 0.348130i
\(625\) 1.00000 0.0400000
\(626\) 12.8065 + 22.1815i 0.511851 + 0.886551i
\(627\) −20.7568 + 5.89163i −0.828945 + 0.235289i
\(628\) 6.17457 + 3.56489i 0.246392 + 0.142255i
\(629\) 60.6516 2.41834
\(630\) 7.21842 + 3.30068i 0.287589 + 0.131502i
\(631\) −12.9441 −0.515297 −0.257648 0.966239i \(-0.582948\pi\)
−0.257648 + 0.966239i \(0.582948\pi\)
\(632\) 6.72991 + 3.88551i 0.267701 + 0.154557i
\(633\) −9.65762 9.37651i −0.383856 0.372683i
\(634\) 9.79975 + 16.9737i 0.389198 + 0.674110i
\(635\) 4.10553 0.162923
\(636\) 8.92616 + 2.25102i 0.353945 + 0.0892588i
\(637\) −28.9959 + 22.2254i −1.14886 + 0.880602i
\(638\) 32.8167i 1.29922i
\(639\) 16.4153 30.4766i 0.649379 1.20564i
\(640\) 0.866025 + 0.500000i 0.0342327 + 0.0197642i
\(641\) 50.1023i 1.97892i −0.144797 0.989461i \(-0.546253\pi\)
0.144797 0.989461i \(-0.453747\pi\)
\(642\) 5.11856 20.2971i 0.202014 0.801061i
\(643\) 13.3473 + 7.70607i 0.526366 + 0.303898i 0.739535 0.673118i \(-0.235045\pi\)
−0.213169 + 0.977015i \(0.568379\pi\)
\(644\) 4.08013 8.26828i 0.160780 0.325816i
\(645\) 3.41805 0.970182i 0.134585 0.0382009i
\(646\) 9.73910 16.8686i 0.383180 0.663687i
\(647\) −8.95179 + 15.5050i −0.351931 + 0.609563i −0.986588 0.163232i \(-0.947808\pi\)
0.634657 + 0.772794i \(0.281142\pi\)
\(648\) 7.51497 4.95230i 0.295216 0.194545i
\(649\) −4.11162 + 2.37384i −0.161395 + 0.0931815i
\(650\) 2.60957 + 4.51990i 0.102356 + 0.177285i
\(651\) −7.33416 6.24600i −0.287448 0.244800i
\(652\) 1.11012 1.92279i 0.0434758 0.0753024i
\(653\) 0.406480i 0.0159068i −0.999968 0.00795339i \(-0.997468\pi\)
0.999968 0.00795339i \(-0.00253167\pi\)
\(654\) 1.56375 + 5.50923i 0.0611473 + 0.215428i
\(655\) −19.4136 −0.758554
\(656\) 2.90122 + 5.02506i 0.113274 + 0.196196i
\(657\) −23.9996 38.8704i −0.936313 1.51648i
\(658\) −12.1000 + 24.5204i −0.471709 + 0.955905i
\(659\) −17.3817 + 10.0353i −0.677093 + 0.390920i −0.798759 0.601651i \(-0.794510\pi\)
0.121666 + 0.992571i \(0.461176\pi\)
\(660\) 2.09905 + 7.39514i 0.0817053 + 0.287855i
\(661\) −1.06654 + 0.615764i −0.0414834 + 0.0239505i −0.520598 0.853802i \(-0.674291\pi\)
0.479115 + 0.877752i \(0.340958\pi\)
\(662\) −19.6316 + 11.3343i −0.763005 + 0.440521i
\(663\) −17.1295 60.3488i −0.665254 2.34375i
\(664\) −4.93150 + 2.84720i −0.191379 + 0.110493i
\(665\) −3.28622 + 6.65943i −0.127434 + 0.258242i
\(666\) −12.4336 + 23.0842i −0.481791 + 0.894494i
\(667\) 12.8838 + 22.3154i 0.498862 + 0.864055i
\(668\) 14.5454 0.562779
\(669\) 0.683973 + 2.40970i 0.0264439 + 0.0931644i
\(670\) 4.92801i 0.190386i
\(671\) 13.4152 23.2358i 0.517888 0.897009i
\(672\) 3.48884 + 2.97120i 0.134585 + 0.114617i
\(673\) −12.4710 21.6005i −0.480723 0.832637i 0.519032 0.854755i \(-0.326293\pi\)
−0.999755 + 0.0221176i \(0.992959\pi\)
\(674\) 16.5721 9.56790i 0.638333 0.368542i
\(675\) 3.50790 3.83336i 0.135019 0.147546i
\(676\) −7.11967 + 12.3316i −0.273834 + 0.474294i
\(677\) 3.88825 6.73465i 0.149438 0.258834i −0.781582 0.623802i \(-0.785587\pi\)
0.931020 + 0.364969i \(0.118920\pi\)
\(678\) 5.37604 1.52594i 0.206466 0.0586035i
\(679\) −15.5154 + 31.4414i −0.595425 + 1.20661i
\(680\) −6.00989 3.46981i −0.230469 0.133061i
\(681\) 3.58502 14.2160i 0.137378 0.544757i
\(682\) 9.33000i 0.357264i
\(683\) −29.8265 17.2203i −1.14128 0.658917i −0.194532 0.980896i \(-0.562319\pi\)
−0.946747 + 0.321979i \(0.895652\pi\)
\(684\) 4.42373 + 7.16479i 0.169146 + 0.273953i
\(685\) 9.19632i 0.351373i
\(686\) −5.96680 + 17.5327i −0.227814 + 0.669403i
\(687\) 23.1493 + 5.83785i 0.883202 + 0.222728i
\(688\) 2.05136 0.0782075
\(689\) 13.8695 + 24.0227i 0.528386 + 0.915191i
\(690\) −4.33068 4.20463i −0.164866 0.160067i
\(691\) −0.603200 0.348258i −0.0229468 0.0132483i 0.488483 0.872574i \(-0.337551\pi\)
−0.511430 + 0.859325i \(0.670884\pi\)
\(692\) −2.50714 −0.0953073
\(693\) 3.33196 + 35.0696i 0.126571 + 1.33218i
\(694\) −0.512308 −0.0194470
\(695\) −8.90078 5.13887i −0.337626 0.194928i
\(696\) −12.3202 + 3.49698i −0.466996 + 0.132553i
\(697\) −20.1333 34.8720i −0.762605 1.32087i
\(698\) 1.31837 0.0499011
\(699\) 9.13966 + 32.1999i 0.345694 + 1.21791i
\(700\) 2.37260 + 1.17080i 0.0896758 + 0.0442522i
\(701\) 40.4903i 1.52930i 0.644447 + 0.764649i \(0.277088\pi\)
−0.644447 + 0.764649i \(0.722912\pi\)
\(702\) 26.4805 + 5.85197i 0.999442 + 0.220868i
\(703\) −21.2447 12.2656i −0.801259 0.462607i
\(704\) 4.43825i 0.167273i
\(705\) 12.8431 + 12.4692i 0.483698 + 0.469619i
\(706\) −10.6523 6.15009i −0.400903 0.231462i
\(707\) 39.8338 26.6011i 1.49810 1.00044i
\(708\) 1.32934 + 1.29065i 0.0499597 + 0.0485054i
\(709\) −17.9957 + 31.1695i −0.675844 + 1.17060i 0.300377 + 0.953820i \(0.402887\pi\)
−0.976221 + 0.216776i \(0.930446\pi\)
\(710\) 5.76938 9.99286i 0.216521 0.375025i
\(711\) 19.8367 12.2477i 0.743934 0.459324i
\(712\) 7.22198 4.16961i 0.270655 0.156263i
\(713\) 3.66295 + 6.34442i 0.137179 + 0.237600i
\(714\) −24.2112 20.6190i −0.906081 0.771647i
\(715\) −11.5819 + 20.0604i −0.433139 + 0.750218i
\(716\) 7.44796i 0.278343i
\(717\) 9.94965 10.2479i 0.371576 0.382716i
\(718\) −23.8295 −0.889310
\(719\) −2.71108 4.69573i −0.101106 0.175121i 0.811034 0.584998i \(-0.198905\pi\)
−0.912141 + 0.409877i \(0.865572\pi\)
\(720\) 2.55265 1.57607i 0.0951315 0.0587367i
\(721\) −14.4542 21.6443i −0.538301 0.806077i
\(722\) 9.63178 5.56091i 0.358458 0.206956i
\(723\) 40.1571 + 10.1269i 1.49346 + 0.376624i
\(724\) 5.35698 3.09285i 0.199091 0.114945i
\(725\) −6.40344 + 3.69703i −0.237818 + 0.137304i
\(726\) −10.4944 + 10.8090i −0.389484 + 0.401161i
\(727\) −28.3952 + 16.3940i −1.05312 + 0.608020i −0.923522 0.383547i \(-0.874703\pi\)
−0.129600 + 0.991566i \(0.541369\pi\)
\(728\) 0.899543 + 13.7792i 0.0333393 + 0.510691i
\(729\) −2.38925 26.8941i −0.0884908 0.996077i
\(730\) −7.61374 13.1874i −0.281797 0.488087i
\(731\) −14.2357 −0.526526
\(732\) −10.1529 2.56037i −0.375260 0.0946340i
\(733\) 6.24073i 0.230507i 0.993336 + 0.115253i \(0.0367680\pi\)
−0.993336 + 0.115253i \(0.963232\pi\)
\(734\) 15.0597 26.0842i 0.555864 0.962784i
\(735\) 9.72308 + 7.24304i 0.358641 + 0.267164i
\(736\) −1.74245 3.01802i −0.0642277 0.111246i
\(737\) −18.9415 + 10.9359i −0.697718 + 0.402828i
\(738\) 17.3997 0.514060i 0.640492 0.0189228i
\(739\) 13.1808 22.8298i 0.484864 0.839809i −0.514985 0.857199i \(-0.672202\pi\)
0.999849 + 0.0173901i \(0.00553572\pi\)
\(740\) −4.36995 + 7.56898i −0.160643 + 0.278241i
\(741\) −6.20438 + 24.6028i −0.227924 + 0.903805i
\(742\) 12.6100 + 6.22266i 0.462929 + 0.228441i
\(743\) −32.8093 18.9425i −1.20366 0.694931i −0.242290 0.970204i \(-0.577899\pi\)
−0.961366 + 0.275273i \(0.911232\pi\)
\(744\) −3.50272 + 0.994216i −0.128416 + 0.0364497i
\(745\) 15.3288i 0.561602i
\(746\) −31.9171 18.4273i −1.16857 0.674673i
\(747\) 0.504489 + 17.0758i 0.0184583 + 0.624769i
\(748\) 30.7997i 1.12615i
\(749\) 14.1496 28.6738i 0.517015 1.04772i
\(750\) 1.20653 1.24270i 0.0440561 0.0453769i
\(751\) 0.439573 0.0160402 0.00802012 0.999968i \(-0.497447\pi\)
0.00802012 + 0.999968i \(0.497447\pi\)
\(752\) 5.16742 + 8.95023i 0.188436 + 0.326381i
\(753\) 9.23597 36.6242i 0.336578 1.33466i
\(754\) −33.4204 19.2953i −1.21710 0.702693i
\(755\) 5.74675 0.209146
\(756\) 12.8109 4.98796i 0.465930 0.181410i
\(757\) −5.35536 −0.194644 −0.0973220 0.995253i \(-0.531028\pi\)
−0.0973220 + 0.995253i \(0.531028\pi\)
\(758\) 2.69079 + 1.55353i 0.0977339 + 0.0564267i
\(759\) 6.55073 25.9761i 0.237776 0.942874i
\(760\) 1.40341 + 2.43077i 0.0509069 + 0.0881733i
\(761\) 1.19842 0.0434429 0.0217214 0.999764i \(-0.493085\pi\)
0.0217214 + 0.999764i \(0.493085\pi\)
\(762\) 4.95343 5.10193i 0.179444 0.184824i
\(763\) 0.569875 + 8.72933i 0.0206308 + 0.316023i
\(764\) 22.9888i 0.831704i
\(765\) −17.7144 + 10.9373i −0.640465 + 0.395440i
\(766\) 9.69416 + 5.59692i 0.350264 + 0.202225i
\(767\) 5.58302i 0.201591i
\(768\) 1.66623 0.472945i 0.0601249 0.0170659i
\(769\) 37.0240 + 21.3758i 1.33512 + 0.770831i 0.986079 0.166277i \(-0.0531745\pi\)
0.349040 + 0.937108i \(0.386508\pi\)
\(770\) 0.764954 + 11.7176i 0.0275670 + 0.422271i
\(771\) 4.26716 16.9209i 0.153678 0.609392i
\(772\) −5.44323 + 9.42795i −0.195906 + 0.339319i
\(773\) −11.5098 + 19.9356i −0.413979 + 0.717032i −0.995321 0.0966270i \(-0.969195\pi\)
0.581342 + 0.813659i \(0.302528\pi\)
\(774\) 2.91831 5.41815i 0.104897 0.194751i
\(775\) −1.82054 + 1.05109i −0.0653958 + 0.0377563i
\(776\) 6.62595 + 11.4765i 0.237858 + 0.411982i
\(777\) −25.9680 + 30.4921i −0.931597 + 1.09390i
\(778\) 11.4996 19.9179i 0.412280 0.714090i
\(779\) 16.2863i 0.583519i
\(780\) 8.76538 + 2.21047i 0.313851 + 0.0791477i
\(781\) 51.2119 1.83251
\(782\) 12.0920 + 20.9439i 0.432408 + 0.748952i
\(783\) −8.29061 + 37.5155i −0.296282 + 1.34069i
\(784\) 4.25845 + 5.55569i 0.152087 + 0.198417i
\(785\) 6.17457 3.56489i 0.220380 0.127236i
\(786\) −23.4231 + 24.1253i −0.835473 + 0.860521i
\(787\) 45.4340 26.2313i 1.61955 0.935046i 0.632511 0.774552i \(-0.282024\pi\)
0.987037 0.160495i \(-0.0513090\pi\)
\(788\) −6.12656 + 3.53717i −0.218250 + 0.126007i
\(789\) 3.31801 + 0.836745i 0.118124 + 0.0297889i
\(790\) 6.72991 3.88551i 0.239439 0.138240i
\(791\) 8.51831 0.556098i 0.302876 0.0197726i
\(792\) 11.7225 + 6.31395i 0.416540 + 0.224356i
\(793\) −15.7755 27.3240i −0.560206 0.970305i
\(794\) 7.81538 0.277358
\(795\) 6.41252 6.60477i 0.227429 0.234247i
\(796\) 18.4715i 0.654706i
\(797\) 23.0129 39.8595i 0.815158 1.41190i −0.0940562 0.995567i \(-0.529983\pi\)
0.909214 0.416328i \(-0.136683\pi\)
\(798\) 4.31075 + 12.1185i 0.152599 + 0.428992i
\(799\) −35.8599 62.1112i −1.26863 2.19734i
\(800\) 0.866025 0.500000i 0.0306186 0.0176777i
\(801\) −0.738803 25.0068i −0.0261043 0.883570i
\(802\) 5.81741 10.0760i 0.205420 0.355797i
\(803\) 33.7917 58.5289i 1.19248 2.06544i
\(804\) 6.12402 + 5.94577i 0.215978 + 0.209691i
\(805\) −5.12047 7.66764i −0.180473 0.270249i
\(806\) −9.50165 5.48578i −0.334681 0.193228i
\(807\) 10.2533 + 9.95480i 0.360932 + 0.350426i
\(808\) 18.1043i 0.636906i
\(809\) 6.56411 + 3.78979i 0.230782 + 0.133242i 0.610933 0.791683i \(-0.290795\pi\)
−0.380151 + 0.924924i \(0.624128\pi\)
\(810\) −0.531331 8.98430i −0.0186691 0.315676i
\(811\) 27.5654i 0.967951i 0.875081 + 0.483976i \(0.160808\pi\)
−0.875081 + 0.483976i \(0.839192\pi\)
\(812\) −19.5213 + 1.27440i −0.685063 + 0.0447227i
\(813\) 13.5916 + 47.8844i 0.476677 + 1.67938i
\(814\) −38.7899 −1.35958
\(815\) −1.11012 1.92279i −0.0388860 0.0673525i
\(816\) −11.5630 + 3.28206i −0.404786 + 0.114895i
\(817\) 4.98639 + 2.87890i 0.174452 + 0.100720i
\(818\) −27.9756 −0.978145
\(819\) 37.6739 + 17.2267i 1.31643 + 0.601949i
\(820\) 5.80244 0.202630
\(821\) 27.7304 + 16.0101i 0.967796 + 0.558757i 0.898564 0.438843i \(-0.144612\pi\)
0.0692324 + 0.997601i \(0.477945\pi\)
\(822\) 11.4282 + 11.0956i 0.398606 + 0.387003i
\(823\) 16.9369 + 29.3356i 0.590384 + 1.02258i 0.994181 + 0.107727i \(0.0343572\pi\)
−0.403796 + 0.914849i \(0.632309\pi\)
\(824\) −9.83724 −0.342697
\(825\) 7.45390 + 1.87974i 0.259512 + 0.0654443i
\(826\) 1.57177 + 2.35365i 0.0546890 + 0.0818939i
\(827\) 49.6428i 1.72625i −0.504992 0.863124i \(-0.668505\pi\)
0.504992 0.863124i \(-0.331495\pi\)
\(828\) −10.4502 + 0.308741i −0.363168 + 0.0107295i
\(829\) 23.6571 + 13.6584i 0.821646 + 0.474378i 0.850984 0.525192i \(-0.176006\pi\)
−0.0293377 + 0.999570i \(0.509340\pi\)
\(830\) 5.69440i 0.197656i
\(831\) −8.64964 + 34.2991i −0.300053 + 1.18982i
\(832\) 4.51990 + 2.60957i 0.156699 + 0.0904704i
\(833\) −29.5520 38.5543i −1.02392 1.33583i
\(834\) −17.1251 + 4.86080i −0.592993 + 0.168316i
\(835\) 7.27271 12.5967i 0.251683 0.435927i
\(836\) −6.22866 + 10.7884i −0.215423 + 0.373123i
\(837\) −2.35708 + 10.6659i −0.0814725 + 0.368668i
\(838\) −2.78155 + 1.60593i −0.0960872 + 0.0554760i
\(839\) −15.8314 27.4209i −0.546562 0.946673i −0.998507 0.0546273i \(-0.982603\pi\)
0.451945 0.892046i \(-0.350730\pi\)
\(840\) 4.31755 1.53582i 0.148970 0.0529908i
\(841\) 12.8360 22.2327i 0.442622 0.766644i
\(842\) 7.45922i 0.257062i
\(843\) −0.837825 2.95174i −0.0288562 0.101663i
\(844\) −7.77150 −0.267506
\(845\) 7.11967 + 12.3316i 0.244924 + 0.424221i
\(846\) 30.9910 0.915602i 1.06549 0.0314790i
\(847\) −19.1378 + 12.7803i −0.657583 + 0.439136i
\(848\) 4.60281 2.65743i 0.158061 0.0912566i
\(849\) 1.14555 + 4.03589i 0.0393153 + 0.138511i
\(850\) −6.00989 + 3.46981i −0.206137 + 0.119013i
\(851\) 26.3772 15.2289i 0.904198 0.522039i
\(852\) −5.45720 19.2262i −0.186961 0.658680i
\(853\) 8.23214 4.75283i 0.281863 0.162734i −0.352403 0.935848i \(-0.614635\pi\)
0.634267 + 0.773114i \(0.281302\pi\)
\(854\) −14.3430 7.07782i −0.490807 0.242198i
\(855\) 8.41676 0.248666i 0.287847 0.00850420i
\(856\) −6.04270 10.4663i −0.206535 0.357729i
\(857\) −3.35621 −0.114646 −0.0573230 0.998356i \(-0.518256\pi\)
−0.0573230 + 0.998356i \(0.518256\pi\)
\(858\) 10.9552 + 38.5962i 0.374004 + 1.31765i
\(859\) 30.7525i 1.04926i 0.851330 + 0.524631i \(0.175797\pi\)
−0.851330 + 0.524631i \(0.824203\pi\)
\(860\) 1.02568 1.77653i 0.0349755 0.0605793i
\(861\) 26.1517 + 4.80858i 0.891247 + 0.163876i
\(862\) 7.05686 + 12.2228i 0.240358 + 0.416312i
\(863\) 46.5984 26.9036i 1.58623 0.915809i 0.592307 0.805712i \(-0.298217\pi\)
0.993921 0.110097i \(-0.0351162\pi\)
\(864\) 1.12125 5.07374i 0.0381458 0.172612i
\(865\) −1.25357 + 2.17125i −0.0426227 + 0.0738247i
\(866\) 8.96174 15.5222i 0.304532 0.527465i
\(867\) 51.9169 14.7362i 1.76319 0.500466i
\(868\) −5.55003 + 0.362321i −0.188380 + 0.0122980i
\(869\) 29.8690 + 17.2449i 1.01324 + 0.584992i
\(870\) −3.13163 + 12.4181i −0.106172 + 0.421013i
\(871\) 25.7199i 0.871487i
\(872\) 2.86343 + 1.65320i 0.0969679 + 0.0559844i
\(873\) 39.7384 1.17404i 1.34494 0.0397351i
\(874\) 9.78147i 0.330863i
\(875\) 2.20024 1.46933i 0.0743818 0.0496724i
\(876\) −25.5741 6.44934i −0.864069 0.217903i
\(877\) −50.5842 −1.70811 −0.854053 0.520186i \(-0.825863\pi\)
−0.854053 + 0.520186i \(0.825863\pi\)
\(878\) −19.4420 33.6745i −0.656135 1.13646i
\(879\) −13.8814 13.4774i −0.468208 0.454580i
\(880\) 3.84363 + 2.21912i 0.129569 + 0.0748066i
\(881\) −40.0580 −1.34959 −0.674793 0.738007i \(-0.735767\pi\)
−0.674793 + 0.738007i \(0.735767\pi\)
\(882\) 20.7321 3.34394i 0.698085 0.112596i
\(883\) −20.3605 −0.685187 −0.342593 0.939484i \(-0.611305\pi\)
−0.342593 + 0.939484i \(0.611305\pi\)
\(884\) −31.3664 18.1094i −1.05497 0.609085i
\(885\) 1.78240 0.505919i 0.0599148 0.0170063i
\(886\) −13.6113 23.5754i −0.457280 0.792032i
\(887\) 25.8585 0.868245 0.434122 0.900854i \(-0.357059\pi\)
0.434122 + 0.900854i \(0.357059\pi\)
\(888\) 4.13349 + 14.5627i 0.138711 + 0.488692i
\(889\) 9.03317 6.03238i 0.302963 0.202320i
\(890\) 8.33922i 0.279531i
\(891\) 33.3533 21.9795i 1.11738 0.736342i
\(892\) 1.25245 + 0.723100i 0.0419350 + 0.0242112i
\(893\) 29.0079i 0.970713i
\(894\) 19.0490 + 18.4945i 0.637094 + 0.618549i
\(895\) 6.45012 + 3.72398i 0.215604 + 0.124479i
\(896\) 2.64013 0.172355i 0.0882006 0.00575797i
\(897\) −22.6024 21.9445i −0.754672 0.732706i
\(898\) −8.29228 + 14.3626i −0.276717 + 0.479288i
\(899\) 7.77182 13.4612i 0.259205 0.448956i
\(900\) −0.0885938 2.99869i −0.00295313 0.0999564i
\(901\) −31.9417 + 18.4416i −1.06413 + 0.614378i
\(902\) 12.8763 + 22.3024i 0.428735 + 0.742590i
\(903\) 6.09501 7.15687i 0.202829 0.238166i
\(904\) 1.61324 2.79421i 0.0536554 0.0929339i
\(905\) 6.18571i 0.205620i
\(906\) 6.93360 7.14147i 0.230353 0.237260i
\(907\) 37.0791 1.23119 0.615595 0.788062i \(-0.288916\pi\)
0.615595 + 0.788062i \(0.288916\pi\)
\(908\) −4.23228 7.33052i −0.140453 0.243272i
\(909\) −47.8177 25.7555i −1.58601 0.854256i
\(910\) 12.3829 + 6.11057i 0.410489 + 0.202563i
\(911\) −18.8303 + 10.8717i −0.623874 + 0.360194i −0.778376 0.627799i \(-0.783956\pi\)
0.154502 + 0.987993i \(0.450623\pi\)
\(912\) 4.71395 + 1.18878i 0.156095 + 0.0393643i
\(913\) −21.8872 + 12.6366i −0.724360 + 0.418210i
\(914\) 15.1871 8.76829i 0.502345 0.290029i
\(915\) −7.29377 + 7.51244i −0.241125 + 0.248354i
\(916\) 11.9370 6.89186i 0.394411 0.227713i
\(917\) −42.7148 + 28.5250i −1.41057 + 0.941980i
\(918\) −7.78107 + 35.2098i −0.256814 + 1.16210i
\(919\) 9.93377 + 17.2058i 0.327685 + 0.567567i 0.982052 0.188610i \(-0.0603983\pi\)
−0.654367 + 0.756177i \(0.727065\pi\)
\(920\) −3.48491 −0.114894
\(921\) −4.17517 1.05290i −0.137577 0.0346944i
\(922\) 35.7467i 1.17725i
\(923\) 30.1112 52.1541i 0.991121 1.71667i
\(924\) 15.4843 + 13.1869i 0.509396 + 0.433818i
\(925\) 4.36995 + 7.56898i 0.143683 + 0.248867i
\(926\) −17.7886 + 10.2703i −0.584570 + 0.337502i
\(927\) −13.9947 + 25.9825i −0.459645 + 0.853378i
\(928\) −3.69703 + 6.40344i −0.121361 + 0.210203i
\(929\) −9.12389 + 15.8030i −0.299345 + 0.518481i −0.975986 0.217832i \(-0.930102\pi\)
0.676641 + 0.736313i \(0.263435\pi\)
\(930\) −0.890342 + 3.53055i −0.0291955 + 0.115771i
\(931\) 2.55442 + 19.4809i 0.0837177 + 0.638461i
\(932\) 16.7359 + 9.66250i 0.548204 + 0.316506i
\(933\) 11.0315 3.13120i 0.361156 0.102511i
\(934\) 7.09543i 0.232170i
\(935\) −26.6734 15.3999i −0.872312 0.503630i
\(936\) 13.3226 8.22572i 0.435463 0.268866i
\(937\) 33.7791i 1.10351i 0.834005 + 0.551757i \(0.186043\pi\)
−0.834005 + 0.551757i \(0.813957\pi\)
\(938\) 7.24087 + 10.8428i 0.236423 + 0.354031i
\(939\) 30.9027 31.8292i 1.00847 1.03871i
\(940\) 10.3348 0.337085
\(941\) 4.40857 + 7.63587i 0.143715 + 0.248922i 0.928893 0.370348i \(-0.120762\pi\)
−0.785178 + 0.619271i \(0.787428\pi\)
\(942\) 3.01969 11.9743i 0.0983870 0.390142i
\(943\) −17.5118 10.1105i −0.570264 0.329242i
\(944\) 1.06972 0.0348165
\(945\) 2.08577 13.5886i 0.0678502 0.442037i
\(946\) 9.10446 0.296012
\(947\) −28.6235 16.5258i −0.930140 0.537017i −0.0432843 0.999063i \(-0.513782\pi\)
−0.886856 + 0.462046i \(0.847115\pi\)
\(948\) 3.29129 13.0512i 0.106896 0.423884i
\(949\) −39.7371 68.8267i −1.28992 2.23421i
\(950\) 2.80681 0.0910649
\(951\) 23.6473 24.3562i 0.766816 0.789805i
\(952\) −18.3215 + 1.19608i −0.593803 + 0.0387651i
\(953\) 8.17464i 0.264803i −0.991196 0.132401i \(-0.957731\pi\)
0.991196 0.132401i \(-0.0422688\pi\)
\(954\) −0.470864 15.9376i −0.0152448 0.516000i
\(955\) −19.9088 11.4944i −0.644235 0.371949i
\(956\) 8.24653i 0.266712i
\(957\) −54.6801 + 15.5205i −1.76756 + 0.501706i
\(958\) −14.9914 8.65531i −0.484351 0.279640i
\(959\) 13.5124 + 20.2342i 0.436339 + 0.653395i
\(960\) 0.423533 1.67947i 0.0136695 0.0542047i
\(961\) −13.2904 + 23.0197i −0.428723 + 0.742570i
\(962\) −22.8074 + 39.5035i −0.735339 + 1.27364i
\(963\) −36.2404 + 1.07069i −1.16783 + 0.0345025i
\(964\) 20.7072 11.9553i 0.666933 0.385054i
\(965\) 5.44323 + 9.42795i 0.175224 + 0.303496i
\(966\) −15.7065 2.88800i −0.505350 0.0929199i
\(967\) −16.5402 + 28.6485i −0.531899 + 0.921275i 0.467408 + 0.884042i \(0.345188\pi\)
−0.999307 + 0.0372336i \(0.988145\pi\)
\(968\) 8.69804i 0.279566i
\(969\) −32.7130 8.24965i −1.05089 0.265017i
\(970\) 13.2519 0.425493
\(971\) 15.3895 + 26.6554i 0.493873 + 0.855412i 0.999975 0.00706089i \(-0.00224757\pi\)
−0.506102 + 0.862473i \(0.668914\pi\)
\(972\) −11.8058 10.1795i −0.378672 0.326508i
\(973\) −27.1346 + 1.77142i −0.869894 + 0.0567890i
\(974\) 30.9864 17.8900i 0.992870 0.573234i
\(975\) 6.29702 6.48580i 0.201666 0.207712i
\(976\) −5.23536 + 3.02264i −0.167580 + 0.0967522i
\(977\) 33.0891 19.1040i 1.05861 0.611190i 0.133565 0.991040i \(-0.457358\pi\)
0.925048 + 0.379850i \(0.124024\pi\)
\(978\) −3.72884 0.940349i −0.119235 0.0300690i
\(979\) 32.0529 18.5058i 1.02442 0.591447i
\(980\) 6.94059 0.910079i 0.221709 0.0290714i
\(981\) 8.44007 5.21112i 0.269471 0.166378i
\(982\) −13.9109 24.0944i −0.443914 0.768882i
\(983\) −26.4893 −0.844877 −0.422439 0.906391i \(-0.638826\pi\)
−0.422439 + 0.906391i \(0.638826\pi\)
\(984\) 7.00079 7.21067i 0.223177 0.229868i
\(985\) 7.07434i 0.225407i
\(986\) 25.6560 44.4374i 0.817052 1.41518i
\(987\) 46.5793 + 8.56465i 1.48264 + 0.272616i
\(988\) 7.32456 + 12.6865i 0.233025 + 0.403612i
\(989\) −6.19105 + 3.57441i −0.196864 + 0.113659i
\(990\) 11.3293 6.99499i 0.360068 0.222315i
\(991\) −19.0603 + 33.0135i −0.605471 + 1.04871i 0.386505 + 0.922287i \(0.373682\pi\)
−0.991977 + 0.126420i \(0.959651\pi\)
\(992\) −1.05109 + 1.82054i −0.0333721 + 0.0578023i
\(993\) 28.1703 + 27.3503i 0.893957 + 0.867936i
\(994\) −1.98876 30.4639i −0.0630797 0.966255i
\(995\) 15.9968 + 9.23577i 0.507133 + 0.292794i
\(996\) 7.07642 + 6.87044i 0.224225 + 0.217698i
\(997\) 30.3486i 0.961149i −0.876954 0.480574i \(-0.840428\pi\)
0.876954 0.480574i \(-0.159572\pi\)
\(998\) 9.27358 + 5.35410i 0.293550 + 0.169481i
\(999\) 44.3440 + 9.79965i 1.40298 + 0.310047i
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 630.2.t.c.311.4 32
3.2 odd 2 1890.2.t.c.1151.16 32
7.5 odd 6 630.2.bk.c.131.14 yes 32
9.2 odd 6 630.2.bk.c.101.6 yes 32
9.7 even 3 1890.2.bk.c.521.5 32
21.5 even 6 1890.2.bk.c.341.5 32
63.47 even 6 inner 630.2.t.c.551.4 yes 32
63.61 odd 6 1890.2.t.c.1601.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.t.c.311.4 32 1.1 even 1 trivial
630.2.t.c.551.4 yes 32 63.47 even 6 inner
630.2.bk.c.101.6 yes 32 9.2 odd 6
630.2.bk.c.131.14 yes 32 7.5 odd 6
1890.2.t.c.1151.16 32 3.2 odd 2
1890.2.t.c.1601.16 32 63.61 odd 6
1890.2.bk.c.341.5 32 21.5 even 6
1890.2.bk.c.521.5 32 9.7 even 3