Properties

Label 315.2.bq.a.164.4
Level $315$
Weight $2$
Character 315.164
Analytic conductor $2.515$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(164,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.164");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bq (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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 164.4
Character \(\chi\) \(=\) 315.164
Dual form 315.2.bq.a.194.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.46032 q^{2} +(0.957408 - 1.44339i) q^{3} +4.05317 q^{4} +(-0.494408 + 2.18072i) q^{5} +(-2.35553 + 3.55119i) q^{6} +(-0.227160 - 2.63598i) q^{7} -5.05144 q^{8} +(-1.16674 - 2.76382i) q^{9} +O(q^{10})\) \(q-2.46032 q^{2} +(0.957408 - 1.44339i) q^{3} +4.05317 q^{4} +(-0.494408 + 2.18072i) q^{5} +(-2.35553 + 3.55119i) q^{6} +(-0.227160 - 2.63598i) q^{7} -5.05144 q^{8} +(-1.16674 - 2.76382i) q^{9} +(1.21640 - 5.36528i) q^{10} +(2.30650 - 1.33166i) q^{11} +(3.88053 - 5.85029i) q^{12} +(1.60728 + 2.78389i) q^{13} +(0.558887 + 6.48535i) q^{14} +(2.67428 + 2.80147i) q^{15} +4.32182 q^{16} +(-2.53088 - 1.46120i) q^{17} +(2.87055 + 6.79988i) q^{18} +(5.06365 - 2.92350i) q^{19} +(-2.00392 + 8.83884i) q^{20} +(-4.02223 - 2.19583i) q^{21} +(-5.67472 + 3.27630i) q^{22} +(1.27648 - 2.21092i) q^{23} +(-4.83629 + 7.29119i) q^{24} +(-4.51112 - 2.15634i) q^{25} +(-3.95442 - 6.84926i) q^{26} +(-5.10632 - 0.962046i) q^{27} +(-0.920718 - 10.6841i) q^{28} +(4.19625 + 2.42271i) q^{29} +(-6.57959 - 6.89250i) q^{30} -7.07814i q^{31} -0.530173 q^{32} +(0.286160 - 4.60411i) q^{33} +(6.22676 + 3.59502i) q^{34} +(5.86066 + 0.807876i) q^{35} +(-4.72899 - 11.2022i) q^{36} +(1.59927 - 0.923338i) q^{37} +(-12.4582 + 7.19274i) q^{38} +(5.55706 + 0.345390i) q^{39} +(2.49747 - 11.0158i) q^{40} +(-5.20058 - 9.00767i) q^{41} +(9.89597 + 5.40244i) q^{42} +(2.40794 + 1.39022i) q^{43} +(9.34861 - 5.39742i) q^{44} +(6.60398 - 1.17788i) q^{45} +(-3.14054 + 5.43957i) q^{46} -6.04398i q^{47} +(4.13775 - 6.23807i) q^{48} +(-6.89680 + 1.19758i) q^{49} +(11.0988 + 5.30527i) q^{50} +(-4.53216 + 2.25407i) q^{51} +(6.51457 + 11.2836i) q^{52} +(4.98889 - 8.64101i) q^{53} +(12.5632 + 2.36694i) q^{54} +(1.76363 + 5.68822i) q^{55} +(1.14749 + 13.3155i) q^{56} +(0.628233 - 10.1078i) q^{57} +(-10.3241 - 5.96063i) q^{58} -6.44308 q^{59} +(10.8393 + 11.3548i) q^{60} +8.84605i q^{61} +17.4145i q^{62} +(-7.02035 + 3.70334i) q^{63} -7.33925 q^{64} +(-6.86555 + 2.12866i) q^{65} +(-0.704046 + 11.3276i) q^{66} +9.89679i q^{67} +(-10.2581 - 5.92249i) q^{68} +(-1.96911 - 3.95921i) q^{69} +(-14.4191 - 1.98763i) q^{70} -1.65668i q^{71} +(5.89372 + 13.9613i) q^{72} +(-3.96889 + 6.87432i) q^{73} +(-3.93471 + 2.27171i) q^{74} +(-7.43141 + 4.44681i) q^{75} +(20.5238 - 11.8494i) q^{76} +(-4.03417 - 5.77738i) q^{77} +(-13.6721 - 0.849768i) q^{78} +11.5474 q^{79} +(-2.13674 + 9.42470i) q^{80} +(-6.27743 + 6.44933i) q^{81} +(12.7951 + 22.1617i) q^{82} +(12.2465 + 7.07054i) q^{83} +(-16.3028 - 8.90006i) q^{84} +(4.43776 - 4.79671i) q^{85} +(-5.92429 - 3.42039i) q^{86} +(7.51443 - 3.73730i) q^{87} +(-11.6511 + 6.72678i) q^{88} +(3.53042 + 6.11486i) q^{89} +(-16.2479 + 2.89797i) q^{90} +(6.97318 - 4.86915i) q^{91} +(5.17377 - 8.96123i) q^{92} +(-10.2165 - 6.77667i) q^{93} +14.8701i q^{94} +(3.87184 + 12.4878i) q^{95} +(-0.507591 + 0.765245i) q^{96} +(-1.38925 + 2.40626i) q^{97} +(16.9683 - 2.94643i) q^{98} +(-6.37154 - 4.82105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36} + 12 q^{39} - 30 q^{40} + 6 q^{41} - 84 q^{44} + 21 q^{45} - 18 q^{46} - 8 q^{49} + 30 q^{50} - 24 q^{51} - 60 q^{54} - 78 q^{56} - 12 q^{59} - 45 q^{60} - 8 q^{64} - 24 q^{66} + 60 q^{69} + 15 q^{70} - 30 q^{74} - 48 q^{75} - 48 q^{76} - 16 q^{79} - 69 q^{80} + 36 q^{81} - 90 q^{84} - 7 q^{85} - 12 q^{86} + 72 q^{89} + 33 q^{90} + 20 q^{91} - 60 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46032 −1.73971 −0.869854 0.493310i \(-0.835787\pi\)
−0.869854 + 0.493310i \(0.835787\pi\)
\(3\) 0.957408 1.44339i 0.552760 0.833341i
\(4\) 4.05317 2.02658
\(5\) −0.494408 + 2.18072i −0.221106 + 0.975250i
\(6\) −2.35553 + 3.55119i −0.961640 + 1.44977i
\(7\) −0.227160 2.63598i −0.0858585 0.996307i
\(8\) −5.05144 −1.78595
\(9\) −1.16674 2.76382i −0.388913 0.921274i
\(10\) 1.21640 5.36528i 0.384660 1.69665i
\(11\) 2.30650 1.33166i 0.695435 0.401510i −0.110210 0.993908i \(-0.535152\pi\)
0.805645 + 0.592399i \(0.201819\pi\)
\(12\) 3.88053 5.85029i 1.12021 1.68883i
\(13\) 1.60728 + 2.78389i 0.445779 + 0.772113i 0.998106 0.0615151i \(-0.0195932\pi\)
−0.552327 + 0.833628i \(0.686260\pi\)
\(14\) 0.558887 + 6.48535i 0.149369 + 1.73328i
\(15\) 2.67428 + 2.80147i 0.690497 + 0.723335i
\(16\) 4.32182 1.08046
\(17\) −2.53088 1.46120i −0.613828 0.354394i 0.160634 0.987014i \(-0.448646\pi\)
−0.774462 + 0.632620i \(0.781979\pi\)
\(18\) 2.87055 + 6.79988i 0.676596 + 1.60275i
\(19\) 5.06365 2.92350i 1.16168 0.670697i 0.209975 0.977707i \(-0.432662\pi\)
0.951706 + 0.307009i \(0.0993283\pi\)
\(20\) −2.00392 + 8.83884i −0.448090 + 1.97642i
\(21\) −4.02223 2.19583i −0.877723 0.479169i
\(22\) −5.67472 + 3.27630i −1.20985 + 0.698509i
\(23\) 1.27648 2.21092i 0.266164 0.461009i −0.701704 0.712468i \(-0.747577\pi\)
0.967868 + 0.251459i \(0.0809105\pi\)
\(24\) −4.83629 + 7.29119i −0.987203 + 1.48831i
\(25\) −4.51112 2.15634i −0.902224 0.431267i
\(26\) −3.95442 6.84926i −0.775526 1.34325i
\(27\) −5.10632 0.962046i −0.982711 0.185146i
\(28\) −0.920718 10.6841i −0.173999 2.01910i
\(29\) 4.19625 + 2.42271i 0.779224 + 0.449885i 0.836155 0.548493i \(-0.184798\pi\)
−0.0569312 + 0.998378i \(0.518132\pi\)
\(30\) −6.57959 6.89250i −1.20126 1.25839i
\(31\) 7.07814i 1.27127i −0.771989 0.635636i \(-0.780738\pi\)
0.771989 0.635636i \(-0.219262\pi\)
\(32\) −0.530173 −0.0937221
\(33\) 0.286160 4.60411i 0.0498141 0.801472i
\(34\) 6.22676 + 3.59502i 1.06788 + 0.616541i
\(35\) 5.86066 + 0.807876i 0.990632 + 0.136556i
\(36\) −4.72899 11.2022i −0.788165 1.86704i
\(37\) 1.59927 0.923338i 0.262918 0.151796i −0.362747 0.931888i \(-0.618161\pi\)
0.625665 + 0.780092i \(0.284828\pi\)
\(38\) −12.4582 + 7.19274i −2.02099 + 1.16682i
\(39\) 5.55706 + 0.345390i 0.889842 + 0.0553066i
\(40\) 2.49747 11.0158i 0.394885 1.74175i
\(41\) −5.20058 9.00767i −0.812194 1.40676i −0.911325 0.411688i \(-0.864939\pi\)
0.0991306 0.995074i \(-0.468394\pi\)
\(42\) 9.89597 + 5.40244i 1.52698 + 0.833614i
\(43\) 2.40794 + 1.39022i 0.367207 + 0.212007i 0.672237 0.740336i \(-0.265333\pi\)
−0.305031 + 0.952343i \(0.598667\pi\)
\(44\) 9.34861 5.39742i 1.40936 0.813692i
\(45\) 6.60398 1.17788i 0.984464 0.175589i
\(46\) −3.14054 + 5.43957i −0.463047 + 0.802021i
\(47\) 6.04398i 0.881605i −0.897604 0.440803i \(-0.854694\pi\)
0.897604 0.440803i \(-0.145306\pi\)
\(48\) 4.13775 6.23807i 0.597232 0.900387i
\(49\) −6.89680 + 1.19758i −0.985257 + 0.171083i
\(50\) 11.0988 + 5.30527i 1.56961 + 0.750279i
\(51\) −4.53216 + 2.25407i −0.634630 + 0.315633i
\(52\) 6.51457 + 11.2836i 0.903409 + 1.56475i
\(53\) 4.98889 8.64101i 0.685277 1.18693i −0.288073 0.957608i \(-0.593015\pi\)
0.973350 0.229325i \(-0.0736520\pi\)
\(54\) 12.5632 + 2.36694i 1.70963 + 0.322100i
\(55\) 1.76363 + 5.68822i 0.237807 + 0.766999i
\(56\) 1.14749 + 13.3155i 0.153339 + 1.77936i
\(57\) 0.628233 10.1078i 0.0832115 1.33881i
\(58\) −10.3241 5.96063i −1.35562 0.782669i
\(59\) −6.44308 −0.838818 −0.419409 0.907797i \(-0.637763\pi\)
−0.419409 + 0.907797i \(0.637763\pi\)
\(60\) 10.8393 + 11.3548i 1.39935 + 1.46590i
\(61\) 8.84605i 1.13262i 0.824192 + 0.566310i \(0.191630\pi\)
−0.824192 + 0.566310i \(0.808370\pi\)
\(62\) 17.4145i 2.21164i
\(63\) −7.02035 + 3.70334i −0.884481 + 0.466577i
\(64\) −7.33925 −0.917406
\(65\) −6.86555 + 2.12866i −0.851567 + 0.264028i
\(66\) −0.704046 + 11.3276i −0.0866620 + 1.39433i
\(67\) 9.89679i 1.20908i 0.796573 + 0.604542i \(0.206644\pi\)
−0.796573 + 0.604542i \(0.793356\pi\)
\(68\) −10.2581 5.92249i −1.24397 0.718208i
\(69\) −1.96911 3.95921i −0.237053 0.476632i
\(70\) −14.4191 1.98763i −1.72341 0.237568i
\(71\) 1.65668i 0.196612i −0.995156 0.0983058i \(-0.968658\pi\)
0.995156 0.0983058i \(-0.0313423\pi\)
\(72\) 5.89372 + 13.9613i 0.694582 + 1.64535i
\(73\) −3.96889 + 6.87432i −0.464524 + 0.804579i −0.999180 0.0404909i \(-0.987108\pi\)
0.534656 + 0.845070i \(0.320441\pi\)
\(74\) −3.93471 + 2.27171i −0.457401 + 0.264080i
\(75\) −7.43141 + 4.44681i −0.858106 + 0.513473i
\(76\) 20.5238 11.8494i 2.35424 1.35922i
\(77\) −4.03417 5.77738i −0.459736 0.658394i
\(78\) −13.6721 0.849768i −1.54806 0.0962173i
\(79\) 11.5474 1.29919 0.649594 0.760281i \(-0.274939\pi\)
0.649594 + 0.760281i \(0.274939\pi\)
\(80\) −2.13674 + 9.42470i −0.238895 + 1.05371i
\(81\) −6.27743 + 6.44933i −0.697493 + 0.716592i
\(82\) 12.7951 + 22.1617i 1.41298 + 2.44735i
\(83\) 12.2465 + 7.07054i 1.34423 + 0.776093i 0.987425 0.158086i \(-0.0505322\pi\)
0.356806 + 0.934178i \(0.383866\pi\)
\(84\) −16.3028 8.90006i −1.77878 0.971076i
\(85\) 4.43776 4.79671i 0.481343 0.520277i
\(86\) −5.92429 3.42039i −0.638832 0.368830i
\(87\) 7.51443 3.73730i 0.805631 0.400681i
\(88\) −11.6511 + 6.72678i −1.24201 + 0.717078i
\(89\) 3.53042 + 6.11486i 0.374223 + 0.648174i 0.990210 0.139582i \(-0.0445760\pi\)
−0.615987 + 0.787756i \(0.711243\pi\)
\(90\) −16.2479 + 2.89797i −1.71268 + 0.305473i
\(91\) 6.97318 4.86915i 0.730988 0.510426i
\(92\) 5.17377 8.96123i 0.539403 0.934273i
\(93\) −10.2165 6.77667i −1.05940 0.702708i
\(94\) 14.8701i 1.53374i
\(95\) 3.87184 + 12.4878i 0.397243 + 1.28123i
\(96\) −0.507591 + 0.765245i −0.0518058 + 0.0781025i
\(97\) −1.38925 + 2.40626i −0.141057 + 0.244318i −0.927895 0.372841i \(-0.878384\pi\)
0.786838 + 0.617160i \(0.211717\pi\)
\(98\) 16.9683 2.94643i 1.71406 0.297634i
\(99\) −6.37154 4.82105i −0.640364 0.484534i
\(100\) −18.2843 8.73998i −1.82843 0.873998i
\(101\) 6.65586 + 11.5283i 0.662282 + 1.14711i 0.980014 + 0.198926i \(0.0637454\pi\)
−0.317732 + 0.948181i \(0.602921\pi\)
\(102\) 11.1506 5.54573i 1.10407 0.549109i
\(103\) 0.862252 1.49346i 0.0849602 0.147155i −0.820414 0.571770i \(-0.806257\pi\)
0.905374 + 0.424614i \(0.139590\pi\)
\(104\) −8.11908 14.0627i −0.796142 1.37896i
\(105\) 6.77712 7.68574i 0.661379 0.750052i
\(106\) −12.2743 + 21.2596i −1.19218 + 2.06492i
\(107\) −3.36690 5.83164i −0.325490 0.563766i 0.656121 0.754656i \(-0.272196\pi\)
−0.981612 + 0.190890i \(0.938863\pi\)
\(108\) −20.6967 3.89933i −1.99155 0.375213i
\(109\) −0.210153 + 0.363996i −0.0201290 + 0.0348645i −0.875914 0.482466i \(-0.839741\pi\)
0.855785 + 0.517331i \(0.173074\pi\)
\(110\) −4.33908 13.9948i −0.413715 1.33435i
\(111\) 0.198417 3.19238i 0.0188329 0.303007i
\(112\) −0.981746 11.3922i −0.0927663 1.07647i
\(113\) 5.14898 + 8.91830i 0.484376 + 0.838963i 0.999839 0.0179484i \(-0.00571348\pi\)
−0.515463 + 0.856912i \(0.672380\pi\)
\(114\) −1.54565 + 24.8684i −0.144764 + 2.32914i
\(115\) 4.19031 + 3.87674i 0.390749 + 0.361508i
\(116\) 17.0081 + 9.81963i 1.57916 + 0.911730i
\(117\) 5.81890 7.69032i 0.537958 0.710970i
\(118\) 15.8520 1.45930
\(119\) −3.27679 + 7.00327i −0.300383 + 0.641989i
\(120\) −13.5090 14.1514i −1.23320 1.29184i
\(121\) −1.95338 + 3.38336i −0.177580 + 0.307578i
\(122\) 21.7641i 1.97043i
\(123\) −17.9806 1.11756i −1.62126 0.100767i
\(124\) 28.6889i 2.57634i
\(125\) 6.93271 8.77141i 0.620080 0.784538i
\(126\) 17.2723 9.11139i 1.53874 0.811707i
\(127\) 12.6225i 1.12007i 0.828470 + 0.560034i \(0.189212\pi\)
−0.828470 + 0.560034i \(0.810788\pi\)
\(128\) 19.1172 1.68974
\(129\) 4.31201 2.14458i 0.379651 0.188819i
\(130\) 16.8914 5.23718i 1.48148 0.459331i
\(131\) −9.47370 + 16.4089i −0.827721 + 1.43366i 0.0721006 + 0.997397i \(0.477030\pi\)
−0.899822 + 0.436258i \(0.856304\pi\)
\(132\) 1.15986 18.6612i 0.100952 1.62425i
\(133\) −8.85656 12.6836i −0.767961 1.09981i
\(134\) 24.3492i 2.10345i
\(135\) 4.62256 10.6598i 0.397847 0.917452i
\(136\) 12.7846 + 7.38118i 1.09627 + 0.632931i
\(137\) −4.78771 8.29255i −0.409041 0.708481i 0.585741 0.810498i \(-0.300804\pi\)
−0.994783 + 0.102018i \(0.967470\pi\)
\(138\) 4.84464 + 9.74091i 0.412403 + 0.829201i
\(139\) 0.892139 0.515077i 0.0756703 0.0436882i −0.461687 0.887043i \(-0.652756\pi\)
0.537358 + 0.843354i \(0.319423\pi\)
\(140\) 23.7542 + 3.27446i 2.00760 + 0.276742i
\(141\) −8.72381 5.78655i −0.734677 0.487316i
\(142\) 4.07596i 0.342047i
\(143\) 7.41437 + 4.28069i 0.620021 + 0.357969i
\(144\) −5.04244 11.9447i −0.420204 0.995396i
\(145\) −7.35791 + 7.95306i −0.611042 + 0.660466i
\(146\) 9.76474 16.9130i 0.808136 1.39973i
\(147\) −4.87447 + 11.1013i −0.402040 + 0.915622i
\(148\) 6.48210 3.74244i 0.532825 0.307627i
\(149\) 9.08780 + 5.24684i 0.744502 + 0.429838i 0.823704 0.567020i \(-0.191904\pi\)
−0.0792021 + 0.996859i \(0.525237\pi\)
\(150\) 18.2836 10.9406i 1.49285 0.893293i
\(151\) −12.1828 21.1012i −0.991419 1.71719i −0.608917 0.793234i \(-0.708396\pi\)
−0.382503 0.923954i \(-0.624938\pi\)
\(152\) −25.5787 + 14.7679i −2.07471 + 1.19783i
\(153\) −1.08563 + 8.69974i −0.0877678 + 0.703332i
\(154\) 9.92533 + 14.2142i 0.799806 + 1.14541i
\(155\) 15.4355 + 3.49949i 1.23981 + 0.281086i
\(156\) 22.5237 + 1.39992i 1.80334 + 0.112083i
\(157\) 0.839436 0.0669943 0.0334972 0.999439i \(-0.489336\pi\)
0.0334972 + 0.999439i \(0.489336\pi\)
\(158\) −28.4104 −2.26021
\(159\) −7.69593 15.4739i −0.610327 1.22716i
\(160\) 0.262122 1.15616i 0.0207225 0.0914025i
\(161\) −6.11791 2.86253i −0.482159 0.225599i
\(162\) 15.4445 15.8674i 1.21343 1.24666i
\(163\) 4.78296 2.76144i 0.374630 0.216293i −0.300849 0.953672i \(-0.597270\pi\)
0.675479 + 0.737379i \(0.263937\pi\)
\(164\) −21.0788 36.5096i −1.64598 2.85092i
\(165\) 9.89881 + 2.90035i 0.770622 + 0.225792i
\(166\) −30.1304 17.3958i −2.33857 1.35017i
\(167\) −14.3387 + 8.27845i −1.10956 + 0.640606i −0.938716 0.344692i \(-0.887983\pi\)
−0.170846 + 0.985298i \(0.554650\pi\)
\(168\) 20.3181 + 11.0921i 1.56757 + 0.855774i
\(169\) 1.33330 2.30934i 0.102561 0.177642i
\(170\) −10.9183 + 11.8014i −0.837396 + 0.905129i
\(171\) −13.9880 10.5841i −1.06969 0.809384i
\(172\) 9.75976 + 5.63480i 0.744175 + 0.429650i
\(173\) 17.7064i 1.34619i 0.739554 + 0.673097i \(0.235037\pi\)
−0.739554 + 0.673097i \(0.764963\pi\)
\(174\) −18.4879 + 9.19495i −1.40156 + 0.697067i
\(175\) −4.65931 + 12.3811i −0.352211 + 0.935921i
\(176\) 9.96826 5.75518i 0.751386 0.433813i
\(177\) −6.16866 + 9.29987i −0.463665 + 0.699021i
\(178\) −8.68595 15.0445i −0.651039 1.12763i
\(179\) −5.05552 2.91880i −0.377867 0.218162i 0.299023 0.954246i \(-0.403339\pi\)
−0.676890 + 0.736084i \(0.736673\pi\)
\(180\) 26.7670 4.77416i 1.99510 0.355845i
\(181\) 13.1595i 0.978136i 0.872246 + 0.489068i \(0.162663\pi\)
−0.872246 + 0.489068i \(0.837337\pi\)
\(182\) −17.1562 + 11.9797i −1.27170 + 0.887992i
\(183\) 12.7683 + 8.46928i 0.943859 + 0.626067i
\(184\) −6.44805 + 11.1683i −0.475356 + 0.823341i
\(185\) 1.22286 + 3.94407i 0.0899061 + 0.289974i
\(186\) 25.1359 + 16.6728i 1.84305 + 1.22251i
\(187\) −7.78328 −0.569170
\(188\) 24.4973i 1.78665i
\(189\) −1.37598 + 13.6787i −0.100088 + 0.994979i
\(190\) −9.52596 30.7241i −0.691086 2.22896i
\(191\) 0.705961i 0.0510816i 0.999674 + 0.0255408i \(0.00813077\pi\)
−0.999674 + 0.0255408i \(0.991869\pi\)
\(192\) −7.02665 + 10.5934i −0.507105 + 0.764512i
\(193\) 19.6345i 1.41332i −0.707553 0.706660i \(-0.750201\pi\)
0.707553 0.706660i \(-0.249799\pi\)
\(194\) 3.41801 5.92016i 0.245399 0.425043i
\(195\) −3.50065 + 11.9477i −0.250687 + 0.855589i
\(196\) −27.9539 + 4.85399i −1.99670 + 0.346714i
\(197\) 11.7246 0.835344 0.417672 0.908598i \(-0.362846\pi\)
0.417672 + 0.908598i \(0.362846\pi\)
\(198\) 15.6760 + 11.8613i 1.11405 + 0.842947i
\(199\) −2.41637 1.39509i −0.171292 0.0988953i 0.411903 0.911228i \(-0.364864\pi\)
−0.583195 + 0.812332i \(0.698198\pi\)
\(200\) 22.7877 + 10.8926i 1.61133 + 0.770223i
\(201\) 14.2849 + 9.47526i 1.00758 + 0.668333i
\(202\) −16.3755 28.3632i −1.15218 1.99563i
\(203\) 5.43299 11.6116i 0.381321 0.814973i
\(204\) −18.3696 + 9.13612i −1.28613 + 0.639657i
\(205\) 22.2145 6.88757i 1.55153 0.481049i
\(206\) −2.12141 + 3.67440i −0.147806 + 0.256007i
\(207\) −7.59991 0.948383i −0.528231 0.0659172i
\(208\) 6.94638 + 12.0315i 0.481645 + 0.834233i
\(209\) 7.78620 13.4861i 0.538583 0.932853i
\(210\) −16.6739 + 18.9094i −1.15061 + 1.30487i
\(211\) 9.03985 + 15.6575i 0.622329 + 1.07791i 0.989051 + 0.147575i \(0.0471467\pi\)
−0.366722 + 0.930331i \(0.619520\pi\)
\(212\) 20.2208 35.0234i 1.38877 2.40542i
\(213\) −2.39123 1.58612i −0.163844 0.108679i
\(214\) 8.28364 + 14.3477i 0.566258 + 0.980788i
\(215\) −4.22220 + 4.56371i −0.287951 + 0.311242i
\(216\) 25.7943 + 4.85972i 1.75508 + 0.330662i
\(217\) −18.6578 + 1.60787i −1.26658 + 0.109149i
\(218\) 0.517043 0.895545i 0.0350186 0.0606540i
\(219\) 6.12247 + 12.3102i 0.413718 + 0.831845i
\(220\) 7.14827 + 23.0553i 0.481936 + 1.55439i
\(221\) 9.39425i 0.631925i
\(222\) −0.488168 + 7.85426i −0.0327637 + 0.527144i
\(223\) −4.45382 + 7.71425i −0.298250 + 0.516584i −0.975736 0.218952i \(-0.929736\pi\)
0.677486 + 0.735536i \(0.263070\pi\)
\(224\) 0.120434 + 1.39752i 0.00804684 + 0.0933761i
\(225\) −0.696422 + 14.9838i −0.0464281 + 0.998922i
\(226\) −12.6681 21.9419i −0.842672 1.45955i
\(227\) −12.8775 + 7.43486i −0.854713 + 0.493469i −0.862238 0.506503i \(-0.830938\pi\)
0.00752533 + 0.999972i \(0.497605\pi\)
\(228\) 2.54633 40.9686i 0.168635 2.71321i
\(229\) −13.1745 7.60628i −0.870593 0.502637i −0.00304789 0.999995i \(-0.500970\pi\)
−0.867545 + 0.497358i \(0.834304\pi\)
\(230\) −10.3095 9.53802i −0.679788 0.628918i
\(231\) −12.2013 + 0.291557i −0.802790 + 0.0191830i
\(232\) −21.1971 12.2382i −1.39166 0.803474i
\(233\) −4.91804 8.51830i −0.322192 0.558052i 0.658748 0.752363i \(-0.271086\pi\)
−0.980940 + 0.194311i \(0.937753\pi\)
\(234\) −14.3164 + 18.9206i −0.935890 + 1.23688i
\(235\) 13.1803 + 2.98819i 0.859785 + 0.194928i
\(236\) −26.1149 −1.69993
\(237\) 11.0556 16.6674i 0.718139 1.08267i
\(238\) 8.06194 17.2303i 0.522578 1.11687i
\(239\) −0.889843 + 0.513751i −0.0575591 + 0.0332318i −0.528503 0.848931i \(-0.677247\pi\)
0.470944 + 0.882163i \(0.343913\pi\)
\(240\) 11.5578 + 12.1074i 0.746051 + 0.781531i
\(241\) −1.27009 + 0.733285i −0.0818135 + 0.0472350i −0.540349 0.841441i \(-0.681708\pi\)
0.458535 + 0.888676i \(0.348374\pi\)
\(242\) 4.80594 8.32414i 0.308938 0.535096i
\(243\) 3.29882 + 15.2354i 0.211619 + 0.977352i
\(244\) 35.8545i 2.29535i
\(245\) 0.798238 15.6321i 0.0509975 0.998699i
\(246\) 44.2381 + 2.74954i 2.82052 + 0.175305i
\(247\) 16.2774 + 9.39778i 1.03571 + 0.597966i
\(248\) 35.7548i 2.27043i
\(249\) 21.9305 10.9071i 1.38979 0.691210i
\(250\) −17.0567 + 21.5804i −1.07876 + 1.36487i
\(251\) −5.93611 −0.374684 −0.187342 0.982295i \(-0.559987\pi\)
−0.187342 + 0.982295i \(0.559987\pi\)
\(252\) −28.4546 + 15.0102i −1.79247 + 0.945556i
\(253\) 6.79931i 0.427469i
\(254\) 31.0554i 1.94859i
\(255\) −2.67477 10.9978i −0.167501 0.688711i
\(256\) −32.3560 −2.02225
\(257\) −0.523767 0.302397i −0.0326717 0.0188630i 0.483575 0.875303i \(-0.339338\pi\)
−0.516247 + 0.856440i \(0.672671\pi\)
\(258\) −10.6089 + 5.27634i −0.660482 + 0.328491i
\(259\) −2.79719 4.00590i −0.173809 0.248914i
\(260\) −27.8272 + 8.62781i −1.72577 + 0.535074i
\(261\) 1.80000 14.4244i 0.111417 0.892845i
\(262\) 23.3083 40.3712i 1.43999 2.49414i
\(263\) 9.89547 + 17.1394i 0.610181 + 1.05686i 0.991210 + 0.132301i \(0.0422364\pi\)
−0.381029 + 0.924563i \(0.624430\pi\)
\(264\) −1.44552 + 23.2574i −0.0889658 + 1.43139i
\(265\) 16.3771 + 15.1516i 1.00604 + 0.930754i
\(266\) 21.7899 + 31.2057i 1.33603 + 1.91334i
\(267\) 12.2062 + 0.758653i 0.747005 + 0.0464288i
\(268\) 40.1133i 2.45031i
\(269\) −10.1969 + 17.6615i −0.621714 + 1.07684i 0.367452 + 0.930042i \(0.380230\pi\)
−0.989166 + 0.146798i \(0.953103\pi\)
\(270\) −11.3730 + 26.2266i −0.692137 + 1.59610i
\(271\) 10.4073 6.00866i 0.632198 0.365000i −0.149405 0.988776i \(-0.547736\pi\)
0.781603 + 0.623776i \(0.214402\pi\)
\(272\) −10.9380 6.31505i −0.663213 0.382906i
\(273\) −0.351903 14.7268i −0.0212981 0.891304i
\(274\) 11.7793 + 20.4023i 0.711613 + 1.23255i
\(275\) −13.2764 + 1.03368i −0.800596 + 0.0623335i
\(276\) −7.98113 16.0473i −0.480408 0.965935i
\(277\) 12.0348 6.94832i 0.723104 0.417484i −0.0927903 0.995686i \(-0.529579\pi\)
0.815894 + 0.578202i \(0.196245\pi\)
\(278\) −2.19495 + 1.26725i −0.131644 + 0.0760048i
\(279\) −19.5627 + 8.25835i −1.17119 + 0.494415i
\(280\) −29.6048 4.08094i −1.76922 0.243883i
\(281\) 9.08163 + 5.24328i 0.541765 + 0.312788i 0.745794 0.666177i \(-0.232070\pi\)
−0.204029 + 0.978965i \(0.565404\pi\)
\(282\) 21.4633 + 14.2368i 1.27812 + 0.847787i
\(283\) −1.25858 −0.0748151 −0.0374075 0.999300i \(-0.511910\pi\)
−0.0374075 + 0.999300i \(0.511910\pi\)
\(284\) 6.71479i 0.398450i
\(285\) 21.7317 + 6.36738i 1.28728 + 0.377171i
\(286\) −18.2417 10.5319i −1.07866 0.622762i
\(287\) −22.5627 + 15.7548i −1.33183 + 0.929978i
\(288\) 0.618574 + 1.46530i 0.0364498 + 0.0863438i
\(289\) −4.22978 7.32619i −0.248810 0.430952i
\(290\) 18.1028 19.5671i 1.06303 1.14902i
\(291\) 2.14308 + 4.30900i 0.125630 + 0.252598i
\(292\) −16.0866 + 27.8628i −0.941396 + 1.63055i
\(293\) 8.57020 4.94801i 0.500676 0.289066i −0.228316 0.973587i \(-0.573322\pi\)
0.728993 + 0.684521i \(0.239989\pi\)
\(294\) 11.9928 27.3128i 0.699432 1.59291i
\(295\) 3.18551 14.0506i 0.185468 0.818057i
\(296\) −8.07861 + 4.66419i −0.469560 + 0.271100i
\(297\) −13.0588 + 4.58090i −0.757749 + 0.265811i
\(298\) −22.3589 12.9089i −1.29522 0.747793i
\(299\) 8.20662 0.474601
\(300\) −30.1207 + 18.0237i −1.73902 + 1.04060i
\(301\) 3.11761 6.66308i 0.179696 0.384053i
\(302\) 29.9735 + 51.9156i 1.72478 + 2.98741i
\(303\) 23.0122 + 1.43028i 1.32201 + 0.0821675i
\(304\) 21.8842 12.6349i 1.25515 0.724658i
\(305\) −19.2908 4.37356i −1.10459 0.250429i
\(306\) 2.67099 21.4041i 0.152690 1.22359i
\(307\) −11.8075 −0.673887 −0.336944 0.941525i \(-0.609393\pi\)
−0.336944 + 0.941525i \(0.609393\pi\)
\(308\) −16.3511 23.4167i −0.931693 1.33429i
\(309\) −1.33012 2.67442i −0.0756680 0.152142i
\(310\) −37.9762 8.60986i −2.15690 0.489007i
\(311\) 5.81184 0.329559 0.164780 0.986330i \(-0.447309\pi\)
0.164780 + 0.986330i \(0.447309\pi\)
\(312\) −28.0712 1.74471i −1.58922 0.0987750i
\(313\) 32.5051 1.83730 0.918650 0.395073i \(-0.129281\pi\)
0.918650 + 0.395073i \(0.129281\pi\)
\(314\) −2.06528 −0.116550
\(315\) −4.60504 17.1404i −0.259465 0.965753i
\(316\) 46.8037 2.63291
\(317\) 13.0079 0.730596 0.365298 0.930891i \(-0.380967\pi\)
0.365298 + 0.930891i \(0.380967\pi\)
\(318\) 18.9344 + 38.0707i 1.06179 + 2.13490i
\(319\) 12.9048 0.722533
\(320\) 3.62858 16.0049i 0.202844 0.894700i
\(321\) −11.6408 0.723515i −0.649727 0.0403827i
\(322\) 15.0520 + 7.04275i 0.838816 + 0.392477i
\(323\) −17.0873 −0.950763
\(324\) −25.4435 + 26.1402i −1.41353 + 1.45223i
\(325\) −1.24763 16.0243i −0.0692063 0.888869i
\(326\) −11.7676 + 6.79403i −0.651747 + 0.376286i
\(327\) 0.324185 + 0.651825i 0.0179275 + 0.0360460i
\(328\) 26.2704 + 45.5017i 1.45054 + 2.51241i
\(329\) −15.9318 + 1.37295i −0.878350 + 0.0756933i
\(330\) −24.3542 7.13577i −1.34066 0.392811i
\(331\) 0.177038 0.00973091 0.00486545 0.999988i \(-0.498451\pi\)
0.00486545 + 0.999988i \(0.498451\pi\)
\(332\) 49.6372 + 28.6581i 2.72420 + 1.57282i
\(333\) −4.41787 3.34280i −0.242098 0.183184i
\(334\) 35.2778 20.3676i 1.93031 1.11447i
\(335\) −21.5822 4.89305i −1.17916 0.267336i
\(336\) −17.3834 9.48998i −0.948340 0.517721i
\(337\) −3.55677 + 2.05350i −0.193750 + 0.111861i −0.593737 0.804659i \(-0.702348\pi\)
0.399987 + 0.916521i \(0.369015\pi\)
\(338\) −3.28034 + 5.68171i −0.178427 + 0.309044i
\(339\) 17.8023 + 1.10647i 0.966886 + 0.0600951i
\(340\) 17.9870 19.4419i 0.975482 1.05438i
\(341\) −9.42565 16.3257i −0.510428 0.884087i
\(342\) 34.4150 + 26.0402i 1.86095 + 1.40809i
\(343\) 4.72348 + 17.9078i 0.255044 + 0.966929i
\(344\) −12.1635 7.02263i −0.655814 0.378635i
\(345\) 9.60748 2.33663i 0.517249 0.125800i
\(346\) 43.5634i 2.34199i
\(347\) −7.07823 −0.379979 −0.189990 0.981786i \(-0.560845\pi\)
−0.189990 + 0.981786i \(0.560845\pi\)
\(348\) 30.4572 15.1479i 1.63268 0.812013i
\(349\) 5.53074 + 3.19317i 0.296054 + 0.170927i 0.640669 0.767817i \(-0.278657\pi\)
−0.344615 + 0.938744i \(0.611991\pi\)
\(350\) 11.4634 30.4614i 0.612744 1.62823i
\(351\) −5.52905 15.7617i −0.295119 0.841298i
\(352\) −1.22284 + 0.706008i −0.0651776 + 0.0376303i
\(353\) −7.06503 + 4.07900i −0.376033 + 0.217103i −0.676091 0.736818i \(-0.736327\pi\)
0.300058 + 0.953921i \(0.402994\pi\)
\(354\) 15.1769 22.8806i 0.806641 1.21609i
\(355\) 3.61276 + 0.819075i 0.191745 + 0.0434720i
\(356\) 14.3094 + 24.7845i 0.758395 + 1.31358i
\(357\) 6.97122 + 11.4347i 0.368956 + 0.605186i
\(358\) 12.4382 + 7.18119i 0.657378 + 0.379538i
\(359\) 26.2966 15.1824i 1.38788 0.801294i 0.394806 0.918765i \(-0.370812\pi\)
0.993076 + 0.117470i \(0.0374785\pi\)
\(360\) −33.3596 + 5.95001i −1.75821 + 0.313593i
\(361\) 7.59373 13.1527i 0.399670 0.692248i
\(362\) 32.3765i 1.70167i
\(363\) 3.01332 + 6.05874i 0.158158 + 0.318002i
\(364\) 28.2634 19.7355i 1.48141 1.03442i
\(365\) −13.0288 12.0538i −0.681956 0.630924i
\(366\) −31.4141 20.8371i −1.64204 1.08917i
\(367\) −7.78705 13.4876i −0.406481 0.704045i 0.588012 0.808852i \(-0.299911\pi\)
−0.994493 + 0.104807i \(0.966577\pi\)
\(368\) 5.51670 9.55521i 0.287578 0.498100i
\(369\) −18.8279 + 24.8831i −0.980140 + 1.29536i
\(370\) −3.00861 9.70367i −0.156410 0.504470i
\(371\) −23.9108 11.1877i −1.24139 0.580838i
\(372\) −41.4092 27.4670i −2.14697 1.42410i
\(373\) −28.0068 16.1697i −1.45014 0.837237i −0.451648 0.892196i \(-0.649164\pi\)
−0.998489 + 0.0549593i \(0.982497\pi\)
\(374\) 19.1493 0.990189
\(375\) −6.02312 18.4044i −0.311032 0.950399i
\(376\) 30.5308i 1.57451i
\(377\) 15.5759i 0.802198i
\(378\) 3.38536 33.6539i 0.174124 1.73097i
\(379\) −7.88181 −0.404862 −0.202431 0.979297i \(-0.564884\pi\)
−0.202431 + 0.979297i \(0.564884\pi\)
\(380\) 15.6932 + 50.6153i 0.805045 + 2.59651i
\(381\) 18.2192 + 12.0849i 0.933398 + 0.619128i
\(382\) 1.73689i 0.0888670i
\(383\) −7.97488 4.60430i −0.407497 0.235269i 0.282216 0.959351i \(-0.408930\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(384\) 18.3030 27.5936i 0.934020 1.40813i
\(385\) 14.5934 5.94102i 0.743749 0.302783i
\(386\) 48.3071i 2.45877i
\(387\) 1.03289 8.27714i 0.0525049 0.420751i
\(388\) −5.63087 + 9.75296i −0.285864 + 0.495132i
\(389\) −11.5678 + 6.67865i −0.586509 + 0.338621i −0.763716 0.645552i \(-0.776627\pi\)
0.177207 + 0.984174i \(0.443294\pi\)
\(390\) 8.61272 29.3950i 0.436122 1.48848i
\(391\) −6.46121 + 3.73038i −0.326757 + 0.188653i
\(392\) 34.8388 6.04951i 1.75962 0.305546i
\(393\) 14.6143 + 29.3843i 0.737192 + 1.48224i
\(394\) −28.8463 −1.45325
\(395\) −5.70914 + 25.1818i −0.287258 + 1.26703i
\(396\) −25.8249 19.5405i −1.29775 0.981948i
\(397\) −14.0380 24.3145i −0.704547 1.22031i −0.966855 0.255327i \(-0.917817\pi\)
0.262307 0.964984i \(-0.415517\pi\)
\(398\) 5.94503 + 3.43237i 0.297998 + 0.172049i
\(399\) −26.7867 + 0.640080i −1.34101 + 0.0320441i
\(400\) −19.4963 9.31930i −0.974813 0.465965i
\(401\) 7.46241 + 4.30843i 0.372655 + 0.215153i 0.674618 0.738167i \(-0.264308\pi\)
−0.301963 + 0.953320i \(0.597642\pi\)
\(402\) −35.1454 23.3122i −1.75289 1.16270i
\(403\) 19.7048 11.3766i 0.981565 0.566707i
\(404\) 26.9773 + 46.7260i 1.34217 + 2.32471i
\(405\) −10.9606 16.8780i −0.544636 0.838672i
\(406\) −13.3669 + 28.5682i −0.663387 + 1.41781i
\(407\) 2.45914 4.25935i 0.121895 0.211128i
\(408\) 22.8940 11.3863i 1.13342 0.563706i
\(409\) 0.819612i 0.0405272i 0.999795 + 0.0202636i \(0.00645054\pi\)
−0.999795 + 0.0202636i \(0.993549\pi\)
\(410\) −54.6546 + 16.9456i −2.69920 + 0.836885i
\(411\) −16.5532 1.02883i −0.816507 0.0507486i
\(412\) 3.49485 6.05326i 0.172179 0.298223i
\(413\) 1.46361 + 16.9838i 0.0720196 + 0.835720i
\(414\) 18.6982 + 2.33332i 0.918967 + 0.114677i
\(415\) −21.4737 + 23.2106i −1.05410 + 1.13936i
\(416\) −0.852136 1.47594i −0.0417794 0.0723641i
\(417\) 0.110685 1.78084i 0.00542028 0.0872082i
\(418\) −19.1565 + 33.1801i −0.936976 + 1.62289i
\(419\) 0.359695 + 0.623010i 0.0175723 + 0.0304360i 0.874678 0.484705i \(-0.161073\pi\)
−0.857106 + 0.515141i \(0.827740\pi\)
\(420\) 27.4688 31.1516i 1.34034 1.52004i
\(421\) −4.05616 + 7.02548i −0.197685 + 0.342401i −0.947777 0.318932i \(-0.896676\pi\)
0.750092 + 0.661333i \(0.230009\pi\)
\(422\) −22.2409 38.5224i −1.08267 1.87524i
\(423\) −16.7045 + 7.05175i −0.812200 + 0.342868i
\(424\) −25.2011 + 43.6495i −1.22387 + 2.11981i
\(425\) 8.26625 + 12.0491i 0.400972 + 0.584466i
\(426\) 5.88319 + 3.90235i 0.285041 + 0.189070i
\(427\) 23.3180 2.00947i 1.12844 0.0972451i
\(428\) −13.6466 23.6366i −0.659633 1.14252i
\(429\) 13.2773 6.60346i 0.641033 0.318818i
\(430\) 10.3879 11.2282i 0.500951 0.541471i
\(431\) −10.1849 5.88028i −0.490592 0.283243i 0.234228 0.972182i \(-0.424744\pi\)
−0.724820 + 0.688938i \(0.758077\pi\)
\(432\) −22.0686 4.15779i −1.06178 0.200042i
\(433\) −13.9056 −0.668259 −0.334129 0.942527i \(-0.608442\pi\)
−0.334129 + 0.942527i \(0.608442\pi\)
\(434\) 45.9042 3.95588i 2.20347 0.189888i
\(435\) 4.43483 + 18.2347i 0.212634 + 0.874285i
\(436\) −0.851785 + 1.47533i −0.0407931 + 0.0706557i
\(437\) 14.9271i 0.714061i
\(438\) −15.0632 30.2870i −0.719749 1.44717i
\(439\) 16.3607i 0.780855i 0.920634 + 0.390427i \(0.127673\pi\)
−0.920634 + 0.390427i \(0.872327\pi\)
\(440\) −8.90885 28.7337i −0.424713 1.36982i
\(441\) 11.3567 + 17.6643i 0.540794 + 0.841155i
\(442\) 23.1128i 1.09937i
\(443\) 14.9094 0.708368 0.354184 0.935176i \(-0.384759\pi\)
0.354184 + 0.935176i \(0.384759\pi\)
\(444\) 0.804216 12.9392i 0.0381664 0.614069i
\(445\) −15.0803 + 4.67563i −0.714874 + 0.221646i
\(446\) 10.9578 18.9795i 0.518868 0.898705i
\(447\) 16.2740 8.09386i 0.769732 0.382826i
\(448\) 1.66719 + 19.3461i 0.0787671 + 0.914018i
\(449\) 19.0086i 0.897073i −0.893765 0.448536i \(-0.851945\pi\)
0.893765 0.448536i \(-0.148055\pi\)
\(450\) 1.71342 36.8650i 0.0807713 1.73783i
\(451\) −23.9902 13.8508i −1.12966 0.652208i
\(452\) 20.8697 + 36.1474i 0.981627 + 1.70023i
\(453\) −42.1211 2.61796i −1.97902 0.123003i
\(454\) 31.6829 18.2921i 1.48695 0.858491i
\(455\) 7.17069 + 17.6139i 0.336167 + 0.825754i
\(456\) −3.17348 + 51.0590i −0.148612 + 2.39106i
\(457\) 33.7447i 1.57851i 0.614066 + 0.789254i \(0.289533\pi\)
−0.614066 + 0.789254i \(0.710467\pi\)
\(458\) 32.4134 + 18.7139i 1.51458 + 0.874442i
\(459\) 11.5177 + 9.89618i 0.537601 + 0.461914i
\(460\) 16.9840 + 15.7131i 0.791885 + 0.732626i
\(461\) 15.4785 26.8095i 0.720904 1.24864i −0.239734 0.970839i \(-0.577060\pi\)
0.960638 0.277803i \(-0.0896064\pi\)
\(462\) 30.0192 0.717323i 1.39662 0.0333729i
\(463\) 22.1846 12.8083i 1.03101 0.595252i 0.113734 0.993511i \(-0.463719\pi\)
0.917273 + 0.398259i \(0.130385\pi\)
\(464\) 18.1354 + 10.4705i 0.841917 + 0.486081i
\(465\) 19.8292 18.9289i 0.919556 0.877809i
\(466\) 12.0999 + 20.9577i 0.560519 + 0.970848i
\(467\) 20.3304 11.7377i 0.940777 0.543158i 0.0505730 0.998720i \(-0.483895\pi\)
0.890204 + 0.455563i \(0.150562\pi\)
\(468\) 23.5850 31.1701i 1.09022 1.44084i
\(469\) 26.0877 2.24816i 1.20462 0.103810i
\(470\) −32.4276 7.35190i −1.49577 0.339118i
\(471\) 0.803683 1.21163i 0.0370317 0.0558291i
\(472\) 32.5468 1.49809
\(473\) 7.40519 0.340491
\(474\) −27.2003 + 41.0072i −1.24935 + 1.88352i
\(475\) −29.1468 + 2.26934i −1.33735 + 0.104124i
\(476\) −13.2814 + 28.3854i −0.608750 + 1.30104i
\(477\) −29.7030 3.70659i −1.36000 0.169713i
\(478\) 2.18930 1.26399i 0.100136 0.0578136i
\(479\) 10.4247 + 18.0560i 0.476315 + 0.825002i 0.999632 0.0271366i \(-0.00863892\pi\)
−0.523317 + 0.852138i \(0.675306\pi\)
\(480\) −1.41783 1.48526i −0.0647149 0.0677925i
\(481\) 5.14095 + 2.96813i 0.234407 + 0.135335i
\(482\) 3.12482 1.80411i 0.142332 0.0821752i
\(483\) −9.98909 + 6.08991i −0.454519 + 0.277101i
\(484\) −7.91738 + 13.7133i −0.359881 + 0.623332i
\(485\) −4.56053 4.21925i −0.207083 0.191586i
\(486\) −8.11615 37.4840i −0.368156 1.70031i
\(487\) 2.46902 + 1.42549i 0.111882 + 0.0645950i 0.554897 0.831919i \(-0.312758\pi\)
−0.443015 + 0.896514i \(0.646091\pi\)
\(488\) 44.6853i 2.02281i
\(489\) 0.593408 9.54750i 0.0268349 0.431753i
\(490\) −1.96392 + 38.4600i −0.0887208 + 1.73744i
\(491\) −2.27102 + 1.31117i −0.102490 + 0.0591724i −0.550369 0.834922i \(-0.685513\pi\)
0.447879 + 0.894094i \(0.352180\pi\)
\(492\) −72.8785 4.52964i −3.28562 0.204212i
\(493\) −7.08013 12.2631i −0.318873 0.552304i
\(494\) −40.0476 23.1215i −1.80183 1.04029i
\(495\) 13.6635 11.5110i 0.614130 0.517382i
\(496\) 30.5905i 1.37355i
\(497\) −4.36697 + 0.376332i −0.195886 + 0.0168808i
\(498\) −53.9559 + 26.8350i −2.41782 + 1.20250i
\(499\) −11.2247 + 19.4418i −0.502488 + 0.870335i 0.497508 + 0.867460i \(0.334249\pi\)
−0.999996 + 0.00287566i \(0.999085\pi\)
\(500\) 28.0994 35.5520i 1.25664 1.58993i
\(501\) −1.77896 + 28.6222i −0.0794781 + 1.27874i
\(502\) 14.6047 0.651840
\(503\) 26.1144i 1.16438i 0.813052 + 0.582192i \(0.197805\pi\)
−0.813052 + 0.582192i \(0.802195\pi\)
\(504\) 35.4629 18.7072i 1.57964 0.833284i
\(505\) −28.4307 + 8.81492i −1.26515 + 0.392259i
\(506\) 16.7285i 0.743671i
\(507\) −2.05676 4.13545i −0.0913441 0.183662i
\(508\) 51.1612i 2.26991i
\(509\) 0.143733 0.248952i 0.00637084 0.0110346i −0.862822 0.505507i \(-0.831305\pi\)
0.869193 + 0.494473i \(0.164639\pi\)
\(510\) 6.58079 + 27.0582i 0.291402 + 1.19816i
\(511\) 19.0222 + 8.90036i 0.841491 + 0.393729i
\(512\) 41.3715 1.82838
\(513\) −28.6692 + 10.0569i −1.26577 + 0.444021i
\(514\) 1.28863 + 0.743993i 0.0568392 + 0.0328161i
\(515\) 2.83053 + 2.61871i 0.124728 + 0.115394i
\(516\) 17.4773 8.69233i 0.769394 0.382658i
\(517\) −8.04850 13.9404i −0.353973 0.613099i
\(518\) 6.88198 + 9.85578i 0.302377 + 0.433038i
\(519\) 25.5573 + 16.9523i 1.12184 + 0.744122i
\(520\) 34.6809 10.7528i 1.52086 0.471541i
\(521\) 9.06706 15.7046i 0.397235 0.688031i −0.596149 0.802874i \(-0.703303\pi\)
0.993384 + 0.114843i \(0.0366364\pi\)
\(522\) −4.42856 + 35.4885i −0.193833 + 1.55329i
\(523\) −4.97014 8.60854i −0.217329 0.376425i 0.736661 0.676262i \(-0.236401\pi\)
−0.953991 + 0.299837i \(0.903068\pi\)
\(524\) −38.3985 + 66.5081i −1.67745 + 2.90542i
\(525\) 13.4098 + 18.5789i 0.585253 + 0.810851i
\(526\) −24.3460 42.1685i −1.06154 1.83863i
\(527\) −10.3426 + 17.9139i −0.450530 + 0.780342i
\(528\) 1.23673 19.8981i 0.0538219 0.865955i
\(529\) 8.24122 + 14.2742i 0.358314 + 0.620618i
\(530\) −40.2929 37.2777i −1.75021 1.61924i
\(531\) 7.51740 + 17.8075i 0.326228 + 0.772781i
\(532\) −35.8971 51.4087i −1.55634 2.22885i
\(533\) 16.7176 28.9557i 0.724119 1.25421i
\(534\) −30.0311 1.86653i −1.29957 0.0807726i
\(535\) 14.3818 4.45907i 0.621781 0.192782i
\(536\) 49.9930i 2.15937i
\(537\) −9.05316 + 4.50259i −0.390673 + 0.194301i
\(538\) 25.0875 43.4529i 1.08160 1.87339i
\(539\) −14.3127 + 11.9464i −0.616490 + 0.514567i
\(540\) 18.7360 43.2060i 0.806269 1.85929i
\(541\) 16.8304 + 29.1511i 0.723594 + 1.25330i 0.959550 + 0.281539i \(0.0908447\pi\)
−0.235955 + 0.971764i \(0.575822\pi\)
\(542\) −25.6053 + 14.7832i −1.09984 + 0.634993i
\(543\) 18.9942 + 12.5990i 0.815121 + 0.540674i
\(544\) 1.34180 + 0.774689i 0.0575292 + 0.0332145i
\(545\) −0.689873 0.638248i −0.0295509 0.0273395i
\(546\) 0.865793 + 36.2325i 0.0370525 + 1.55061i
\(547\) −38.7934 22.3974i −1.65869 0.957644i −0.973322 0.229445i \(-0.926309\pi\)
−0.685366 0.728199i \(-0.740358\pi\)
\(548\) −19.4054 33.6111i −0.828956 1.43579i
\(549\) 24.4489 10.3210i 1.04345 0.440491i
\(550\) 32.6641 2.54319i 1.39280 0.108442i
\(551\) 28.3311 1.20695
\(552\) 9.94685 + 19.9997i 0.423366 + 0.851243i
\(553\) −2.62312 30.4388i −0.111546 1.29439i
\(554\) −29.6095 + 17.0951i −1.25799 + 0.726300i
\(555\) 6.86360 + 2.01103i 0.291343 + 0.0853634i
\(556\) 3.61599 2.08769i 0.153352 0.0885378i
\(557\) 14.4946 25.1054i 0.614156 1.06375i −0.376376 0.926467i \(-0.622830\pi\)
0.990532 0.137282i \(-0.0438368\pi\)
\(558\) 48.1305 20.3182i 2.03753 0.860137i
\(559\) 8.93791i 0.378033i
\(560\) 25.3287 + 3.49150i 1.07033 + 0.147543i
\(561\) −7.45177 + 11.2343i −0.314614 + 0.474312i
\(562\) −22.3437 12.9001i −0.942512 0.544160i
\(563\) 12.7952i 0.539255i 0.962965 + 0.269627i \(0.0869005\pi\)
−0.962965 + 0.269627i \(0.913099\pi\)
\(564\) −35.3590 23.4539i −1.48888 0.987586i
\(565\) −21.9941 + 6.81924i −0.925297 + 0.286887i
\(566\) 3.09652 0.130156
\(567\) 18.4263 + 15.0822i 0.773831 + 0.633392i
\(568\) 8.36861i 0.351139i
\(569\) 4.99145i 0.209253i −0.994512 0.104626i \(-0.966635\pi\)
0.994512 0.104626i \(-0.0333647\pi\)
\(570\) −53.4670 15.6658i −2.23949 0.656168i
\(571\) 41.5956 1.74072 0.870361 0.492414i \(-0.163885\pi\)
0.870361 + 0.492414i \(0.163885\pi\)
\(572\) 30.0517 + 17.3504i 1.25652 + 0.725455i
\(573\) 1.01898 + 0.675893i 0.0425683 + 0.0282358i
\(574\) 55.5114 38.7619i 2.31700 1.61789i
\(575\) −10.5258 + 7.22123i −0.438957 + 0.301146i
\(576\) 8.56300 + 20.2844i 0.356792 + 0.845183i
\(577\) 1.85205 3.20784i 0.0771019 0.133544i −0.824897 0.565284i \(-0.808767\pi\)
0.901998 + 0.431739i \(0.142100\pi\)
\(578\) 10.4066 + 18.0248i 0.432857 + 0.749731i
\(579\) −28.3402 18.7982i −1.17778 0.781227i
\(580\) −29.8228 + 32.2351i −1.23833 + 1.33849i
\(581\) 15.8559 33.8878i 0.657813 1.40590i
\(582\) −5.27266 10.6015i −0.218559 0.439447i
\(583\) 26.5739i 1.10058i
\(584\) 20.0486 34.7252i 0.829618 1.43694i
\(585\) 13.8936 + 16.4916i 0.574428 + 0.681843i
\(586\) −21.0854 + 12.1737i −0.871030 + 0.502890i
\(587\) −26.9691 15.5706i −1.11314 0.642669i −0.173496 0.984835i \(-0.555506\pi\)
−0.939640 + 0.342165i \(0.888840\pi\)
\(588\) −19.7570 + 44.9955i −0.814767 + 1.85558i
\(589\) −20.6930 35.8413i −0.852638 1.47681i
\(590\) −7.83737 + 34.5689i −0.322659 + 1.42318i
\(591\) 11.2252 16.9232i 0.461745 0.696126i
\(592\) 6.91175 3.99050i 0.284071 0.164009i
\(593\) −1.87838 + 1.08448i −0.0771357 + 0.0445343i −0.538072 0.842899i \(-0.680847\pi\)
0.460936 + 0.887433i \(0.347514\pi\)
\(594\) 32.1288 11.2705i 1.31826 0.462433i
\(595\) −13.6521 10.6082i −0.559683 0.434896i
\(596\) 36.8344 + 21.2663i 1.50879 + 0.871103i
\(597\) −4.32711 + 2.15209i −0.177097 + 0.0880790i
\(598\) −20.1909 −0.825668
\(599\) 23.2544i 0.950151i 0.879945 + 0.475075i \(0.157579\pi\)
−0.879945 + 0.475075i \(0.842421\pi\)
\(600\) 37.5393 22.4628i 1.53254 0.917040i
\(601\) 14.8394 + 8.56753i 0.605311 + 0.349477i 0.771128 0.636680i \(-0.219693\pi\)
−0.165817 + 0.986157i \(0.553026\pi\)
\(602\) −7.67032 + 16.3933i −0.312619 + 0.668141i
\(603\) 27.3530 11.5470i 1.11390 0.470229i
\(604\) −49.3788 85.5265i −2.00919 3.48003i
\(605\) −6.41240 5.93255i −0.260701 0.241192i
\(606\) −56.6172 3.51895i −2.29992 0.142947i
\(607\) 23.4891 40.6843i 0.953393 1.65132i 0.215389 0.976528i \(-0.430898\pi\)
0.738004 0.674796i \(-0.235769\pi\)
\(608\) −2.68461 + 1.54996i −0.108875 + 0.0628592i
\(609\) −11.5584 18.9589i −0.468371 0.768255i
\(610\) 47.4615 + 10.7603i 1.92166 + 0.435674i
\(611\) 16.8258 9.71437i 0.680698 0.393001i
\(612\) −4.40023 + 35.2615i −0.177869 + 1.42536i
\(613\) −3.19097 1.84230i −0.128882 0.0744100i 0.434173 0.900830i \(-0.357041\pi\)
−0.563055 + 0.826420i \(0.690374\pi\)
\(614\) 29.0501 1.17237
\(615\) 11.3269 38.6583i 0.456743 1.55885i
\(616\) 20.3784 + 29.1841i 0.821067 + 1.17586i
\(617\) −5.72414 9.91450i −0.230445 0.399143i 0.727494 0.686114i \(-0.240685\pi\)
−0.957939 + 0.286971i \(0.907352\pi\)
\(618\) 3.27252 + 6.57992i 0.131640 + 0.264683i
\(619\) 5.77980 3.33697i 0.232310 0.134124i −0.379327 0.925263i \(-0.623845\pi\)
0.611637 + 0.791138i \(0.290511\pi\)
\(620\) 62.5625 + 14.1840i 2.51257 + 0.569643i
\(621\) −8.64510 + 10.0616i −0.346916 + 0.403760i
\(622\) −14.2990 −0.573337
\(623\) 15.3167 10.6952i 0.613650 0.428493i
\(624\) 24.0166 + 1.49271i 0.961434 + 0.0597563i
\(625\) 15.7004 + 19.4550i 0.628017 + 0.778199i
\(626\) −79.9730 −3.19636
\(627\) −12.0111 24.1502i −0.479677 0.964466i
\(628\) 3.40237 0.135769
\(629\) −5.39673 −0.215182
\(630\) 11.3299 + 42.1709i 0.451393 + 1.68013i
\(631\) 37.2873 1.48438 0.742192 0.670187i \(-0.233786\pi\)
0.742192 + 0.670187i \(0.233786\pi\)
\(632\) −58.3312 −2.32029
\(633\) 31.2546 + 1.94258i 1.24226 + 0.0772106i
\(634\) −32.0035 −1.27102
\(635\) −27.5262 6.24068i −1.09235 0.247654i
\(636\) −31.1929 62.7182i −1.23688 2.48694i
\(637\) −14.4190 17.2751i −0.571302 0.684464i
\(638\) −31.7500 −1.25700
\(639\) −4.57877 + 1.93291i −0.181133 + 0.0764649i
\(640\) −9.45171 + 41.6894i −0.373612 + 1.64792i
\(641\) −41.3232 + 23.8580i −1.63217 + 0.942334i −0.648747 + 0.761004i \(0.724707\pi\)
−0.983422 + 0.181329i \(0.941960\pi\)
\(642\) 28.6401 + 1.78008i 1.13034 + 0.0702541i
\(643\) 8.77430 + 15.1975i 0.346025 + 0.599332i 0.985539 0.169447i \(-0.0541980\pi\)
−0.639515 + 0.768779i \(0.720865\pi\)
\(644\) −24.7969 11.6023i −0.977136 0.457196i
\(645\) 2.54484 + 10.4636i 0.100203 + 0.412004i
\(646\) 42.0402 1.65405
\(647\) −12.4689 7.19895i −0.490205 0.283020i 0.234455 0.972127i \(-0.424670\pi\)
−0.724659 + 0.689107i \(0.758003\pi\)
\(648\) 31.7101 32.5784i 1.24569 1.27980i
\(649\) −14.8609 + 8.57997i −0.583343 + 0.336793i
\(650\) 3.06958 + 39.4249i 0.120399 + 1.54637i
\(651\) −15.5424 + 28.4699i −0.609154 + 1.11582i
\(652\) 19.3861 11.1926i 0.759219 0.438336i
\(653\) −1.51264 + 2.61997i −0.0591942 + 0.102527i −0.894104 0.447860i \(-0.852186\pi\)
0.834910 + 0.550387i \(0.185520\pi\)
\(654\) −0.797598 1.60370i −0.0311886 0.0627095i
\(655\) −31.0995 28.7722i −1.21516 1.12422i
\(656\) −22.4760 38.9295i −0.877540 1.51994i
\(657\) 23.6301 + 2.94877i 0.921897 + 0.115042i
\(658\) 39.1973 3.37790i 1.52807 0.131684i
\(659\) −17.9871 10.3849i −0.700678 0.404537i 0.106922 0.994267i \(-0.465900\pi\)
−0.807600 + 0.589731i \(0.799234\pi\)
\(660\) 40.1215 + 11.7556i 1.56173 + 0.457585i
\(661\) 37.6518i 1.46449i 0.681043 + 0.732244i \(0.261527\pi\)
−0.681043 + 0.732244i \(0.738473\pi\)
\(662\) −0.435571 −0.0169289
\(663\) −13.5595 8.99413i −0.526609 0.349303i
\(664\) −61.8626 35.7164i −2.40074 1.38607i
\(665\) 32.0382 13.0428i 1.24239 0.505780i
\(666\) 10.8694 + 8.22435i 0.421180 + 0.318687i
\(667\) 10.7128 6.18505i 0.414802 0.239486i
\(668\) −58.1171 + 33.5539i −2.24862 + 1.29824i
\(669\) 6.87053 + 13.8143i 0.265630 + 0.534091i
\(670\) 53.0990 + 12.0385i 2.05139 + 0.465086i
\(671\) 11.7799 + 20.4034i 0.454758 + 0.787664i
\(672\) 2.13248 + 1.16417i 0.0822620 + 0.0449088i
\(673\) −8.02091 4.63087i −0.309183 0.178507i 0.337378 0.941369i \(-0.390460\pi\)
−0.646561 + 0.762862i \(0.723793\pi\)
\(674\) 8.75078 5.05227i 0.337068 0.194606i
\(675\) 20.9607 + 15.3508i 0.806778 + 0.590854i
\(676\) 5.40408 9.36014i 0.207849 0.360005i
\(677\) 40.7161i 1.56485i 0.622747 + 0.782423i \(0.286017\pi\)
−0.622747 + 0.782423i \(0.713983\pi\)
\(678\) −43.7992 2.72226i −1.68210 0.104548i
\(679\) 6.65843 + 3.11544i 0.255527 + 0.119560i
\(680\) −22.4171 + 24.2303i −0.859657 + 0.929190i
\(681\) −1.59768 + 25.7055i −0.0612233 + 0.985037i
\(682\) 23.1901 + 40.1664i 0.887995 + 1.53805i
\(683\) −8.02097 + 13.8927i −0.306914 + 0.531591i −0.977686 0.210073i \(-0.932630\pi\)
0.670772 + 0.741664i \(0.265963\pi\)
\(684\) −56.6957 42.8990i −2.16782 1.64028i
\(685\) 20.4509 6.34077i 0.781387 0.242268i
\(686\) −11.6213 44.0588i −0.443702 1.68217i
\(687\) −23.5922 + 11.7336i −0.900097 + 0.447663i
\(688\) 10.4067 + 6.00829i 0.396750 + 0.229064i
\(689\) 32.0742 1.22193
\(690\) −23.6375 + 5.74884i −0.899863 + 0.218855i
\(691\) 33.6808i 1.28128i 0.767843 + 0.640638i \(0.221330\pi\)
−0.767843 + 0.640638i \(0.778670\pi\)
\(692\) 71.7671i 2.72818i
\(693\) −11.2608 + 17.8904i −0.427764 + 0.679601i
\(694\) 17.4147 0.661053
\(695\) 0.682160 + 2.20017i 0.0258758 + 0.0834571i
\(696\) −37.9587 + 18.8788i −1.43882 + 0.715597i
\(697\) 30.3964i 1.15135i
\(698\) −13.6074 7.85622i −0.515047 0.297362i
\(699\) −17.0038 1.05684i −0.643142 0.0399734i
\(700\) −18.8850 + 50.1825i −0.713785 + 1.89672i
\(701\) 17.2695i 0.652260i −0.945325 0.326130i \(-0.894255\pi\)
0.945325 0.326130i \(-0.105745\pi\)
\(702\) 13.6032 + 38.7788i 0.513421 + 1.46361i
\(703\) 5.39876 9.35093i 0.203618 0.352677i
\(704\) −16.9280 + 9.77336i −0.637996 + 0.368347i
\(705\) 16.9320 16.1633i 0.637696 0.608746i
\(706\) 17.3822 10.0356i 0.654188 0.377696i
\(707\) 28.8764 20.1635i 1.08601 0.758326i
\(708\) −25.0026 + 37.6939i −0.939655 + 1.41662i
\(709\) −37.6381 −1.41353 −0.706765 0.707449i \(-0.749846\pi\)
−0.706765 + 0.707449i \(0.749846\pi\)
\(710\) −8.88854 2.01519i −0.333581 0.0756286i
\(711\) −13.4729 31.9151i −0.505272 1.19691i
\(712\) −17.8337 30.8889i −0.668346 1.15761i
\(713\) −15.6492 9.03508i −0.586068 0.338366i
\(714\) −17.1514 28.1329i −0.641875 1.05285i
\(715\) −13.0007 + 14.0523i −0.486200 + 0.525526i
\(716\) −20.4908 11.8304i −0.765779 0.442123i
\(717\) −0.110400 + 1.77626i −0.00412297 + 0.0663355i
\(718\) −64.6980 + 37.3534i −2.41451 + 1.39402i
\(719\) 18.6835 + 32.3608i 0.696778 + 1.20686i 0.969578 + 0.244784i \(0.0787171\pi\)
−0.272799 + 0.962071i \(0.587950\pi\)
\(720\) 28.5412 5.09060i 1.06367 0.189716i
\(721\) −4.13261 1.93362i −0.153907 0.0720119i
\(722\) −18.6830 + 32.3599i −0.695309 + 1.20431i
\(723\) −0.157576 + 2.53528i −0.00586032 + 0.0942881i
\(724\) 53.3376i 1.98227i
\(725\) −13.7056 19.9776i −0.509014 0.741951i
\(726\) −7.41372 14.9064i −0.275149 0.553230i
\(727\) −3.14519 + 5.44762i −0.116648 + 0.202041i −0.918438 0.395566i \(-0.870548\pi\)
0.801789 + 0.597607i \(0.203882\pi\)
\(728\) −35.2246 + 24.5962i −1.30551 + 0.911597i
\(729\) 25.1489 + 9.82502i 0.931442 + 0.363890i
\(730\) 32.0549 + 29.6561i 1.18640 + 1.09762i
\(731\) −4.06279 7.03696i −0.150268 0.260271i
\(732\) 51.7520 + 34.3274i 1.91281 + 1.26878i
\(733\) −7.26635 + 12.5857i −0.268389 + 0.464863i −0.968446 0.249224i \(-0.919825\pi\)
0.700057 + 0.714087i \(0.253158\pi\)
\(734\) 19.1586 + 33.1837i 0.707157 + 1.22483i
\(735\) −21.7990 16.1185i −0.804067 0.594539i
\(736\) −0.676753 + 1.17217i −0.0249454 + 0.0432068i
\(737\) 13.1791 + 22.8269i 0.485459 + 0.840840i
\(738\) 46.3226 61.2203i 1.70516 2.25355i
\(739\) 18.0479 31.2599i 0.663903 1.14991i −0.315679 0.948866i \(-0.602232\pi\)
0.979582 0.201047i \(-0.0644344\pi\)
\(740\) 4.95644 + 15.9860i 0.182202 + 0.587656i
\(741\) 29.1488 14.4971i 1.07081 0.532566i
\(742\) 58.8282 + 27.5254i 2.15965 + 1.01049i
\(743\) 8.25448 + 14.2972i 0.302827 + 0.524512i 0.976775 0.214266i \(-0.0687361\pi\)
−0.673948 + 0.738779i \(0.735403\pi\)
\(744\) 51.6081 + 34.2319i 1.89204 + 1.25500i
\(745\) −15.9350 + 17.2239i −0.583813 + 0.631035i
\(746\) 68.9056 + 39.7827i 2.52281 + 1.45655i
\(747\) 5.25319 42.0967i 0.192204 1.54024i
\(748\) −31.5469 −1.15347
\(749\) −14.6073 + 10.1998i −0.533738 + 0.372693i
\(750\) 14.8188 + 45.2807i 0.541105 + 1.65342i
\(751\) 25.1862 43.6238i 0.919058 1.59185i 0.118209 0.992989i \(-0.462285\pi\)
0.800849 0.598866i \(-0.204382\pi\)
\(752\) 26.1210i 0.952535i
\(753\) −5.68328 + 8.56811i −0.207110 + 0.312239i
\(754\) 38.3216i 1.39559i
\(755\) 52.0391 16.1347i 1.89390 0.587201i
\(756\) −5.57709 + 55.4420i −0.202837 + 2.01641i
\(757\) 10.1798i 0.369990i 0.982740 + 0.184995i \(0.0592268\pi\)
−0.982740 + 0.184995i \(0.940773\pi\)
\(758\) 19.3918 0.704341
\(759\) −9.81405 6.50972i −0.356227 0.236288i
\(760\) −19.5584 63.0816i −0.709457 2.28821i
\(761\) 6.15740 10.6649i 0.223206 0.386604i −0.732574 0.680687i \(-0.761681\pi\)
0.955780 + 0.294084i \(0.0950145\pi\)
\(762\) −44.8250 29.7327i −1.62384 1.07710i
\(763\) 1.00722 + 0.471274i 0.0364640 + 0.0170613i
\(764\) 2.86138i 0.103521i
\(765\) −18.4350 6.66868i −0.666518 0.241106i
\(766\) 19.6207 + 11.3280i 0.708926 + 0.409299i
\(767\) −10.3558 17.9368i −0.373928 0.647662i
\(768\) −30.9779 + 46.7022i −1.11782 + 1.68522i
\(769\) −43.8281 + 25.3041i −1.58048 + 0.912491i −0.585692 + 0.810534i \(0.699177\pi\)
−0.994789 + 0.101957i \(0.967490\pi\)
\(770\) −35.9044 + 14.6168i −1.29391 + 0.526753i
\(771\) −0.937935 + 0.466482i −0.0337789 + 0.0167999i
\(772\) 79.5818i 2.86421i
\(773\) −31.7653 18.3397i −1.14252 0.659634i −0.195466 0.980711i \(-0.562622\pi\)
−0.947053 + 0.321077i \(0.895955\pi\)
\(774\) −2.54124 + 20.3644i −0.0913431 + 0.731983i
\(775\) −15.2628 + 31.9304i −0.548258 + 1.14697i
\(776\) 7.01773 12.1551i 0.251922 0.436342i
\(777\) −8.46012 + 0.202158i −0.303505 + 0.00725239i
\(778\) 28.4604 16.4316i 1.02035 0.589102i
\(779\) −52.6679 30.4078i −1.88702 1.08947i
\(780\) −14.1887 + 48.4258i −0.508038 + 1.73392i
\(781\) −2.20613 3.82112i −0.0789414 0.136731i
\(782\) 15.8966 9.17792i 0.568462 0.328202i
\(783\) −19.0966 16.4081i −0.682458 0.586377i
\(784\) −29.8067 + 5.17573i −1.06453 + 0.184847i
\(785\) −0.415024 + 1.83058i −0.0148128 + 0.0653362i
\(786\) −35.9557 72.2947i −1.28250 2.57867i
\(787\) −21.6118 −0.770377 −0.385189 0.922838i \(-0.625864\pi\)
−0.385189 + 0.922838i \(0.625864\pi\)
\(788\) 47.5218 1.69289
\(789\) 34.2129 + 2.12644i 1.21801 + 0.0757034i
\(790\) 14.0463 61.9552i 0.499745 2.20427i
\(791\) 22.3388 15.5985i 0.794277 0.554619i
\(792\) 32.1855 + 24.3533i 1.14366 + 0.865355i
\(793\) −24.6264 + 14.2181i −0.874511 + 0.504899i
\(794\) 34.5380 + 59.8215i 1.22571 + 2.12299i
\(795\) 37.5492 9.13230i 1.33173 0.323889i
\(796\) −9.79394 5.65453i −0.347137 0.200420i
\(797\) −6.31824 + 3.64784i −0.223803 + 0.129213i −0.607710 0.794159i \(-0.707912\pi\)
0.383907 + 0.923372i \(0.374578\pi\)
\(798\) 65.9038 1.57480i 2.33297 0.0557474i
\(799\) −8.83148 + 15.2966i −0.312435 + 0.541154i
\(800\) 2.39167 + 1.14323i 0.0845584 + 0.0404193i
\(801\) 12.7813 16.8919i 0.451605 0.596846i
\(802\) −18.3599 10.6001i −0.648311 0.374303i
\(803\) 21.1408i 0.746043i
\(804\) 57.8991 + 38.4048i 2.04194 + 1.35443i
\(805\) 9.26715 11.9262i 0.326624 0.420344i
\(806\) −48.4800 + 27.9900i −1.70764 + 0.985904i
\(807\) 15.7298 + 31.6273i 0.553716 + 1.11333i
\(808\) −33.6217 58.2344i −1.18281 2.04868i
\(809\) −23.1599 13.3714i −0.814260 0.470113i 0.0341730 0.999416i \(-0.489120\pi\)
−0.848433 + 0.529303i \(0.822454\pi\)
\(810\) 26.9666 + 41.5251i 0.947508 + 1.45904i
\(811\) 17.7557i 0.623487i 0.950166 + 0.311744i \(0.100913\pi\)
−0.950166 + 0.311744i \(0.899087\pi\)
\(812\) 22.0208 47.0637i 0.772778 1.65161i
\(813\) 1.29120 20.7745i 0.0452845 0.728594i
\(814\) −6.05026 + 10.4794i −0.212062 + 0.367301i
\(815\) 3.65721 + 11.7956i 0.128107 + 0.413182i
\(816\) −19.5872 + 9.74169i −0.685689 + 0.341027i
\(817\) 16.2573 0.568770
\(818\) 2.01651i 0.0705055i
\(819\) −21.5934 13.5916i −0.754533 0.474929i
\(820\) 90.0389 27.9165i 3.14429 0.974886i
\(821\) 14.8718i 0.519030i 0.965739 + 0.259515i \(0.0835626\pi\)
−0.965739 + 0.259515i \(0.916437\pi\)
\(822\) 40.7261 + 2.53126i 1.42048 + 0.0882878i
\(823\) 6.01287i 0.209595i 0.994494 + 0.104798i \(0.0334195\pi\)
−0.994494 + 0.104798i \(0.966581\pi\)
\(824\) −4.35561 + 7.54415i −0.151735 + 0.262813i
\(825\) −11.2189 + 20.1526i −0.390592 + 0.701625i
\(826\) −3.60095 41.7857i −0.125293 1.45391i
\(827\) 6.67647 0.232164 0.116082 0.993240i \(-0.462967\pi\)
0.116082 + 0.993240i \(0.462967\pi\)
\(828\) −30.8037 3.84395i −1.07050 0.133587i
\(829\) −30.6385 17.6892i −1.06412 0.614370i −0.137551 0.990495i \(-0.543923\pi\)
−0.926569 + 0.376125i \(0.877256\pi\)
\(830\) 52.8321 57.1054i 1.83383 1.98216i
\(831\) 1.49313 24.0233i 0.0517961 0.833360i
\(832\) −11.7962 20.4317i −0.408961 0.708341i
\(833\) 19.2048 + 7.04669i 0.665408 + 0.244153i
\(834\) −0.272321 + 4.38144i −0.00942970 + 0.151717i
\(835\) −10.9639 35.3617i −0.379420 1.22374i
\(836\) 31.5588 54.6614i 1.09148 1.89050i
\(837\) −6.80950 + 36.1432i −0.235371 + 1.24929i
\(838\) −0.884964 1.53280i −0.0305706 0.0529498i
\(839\) −2.59993 + 4.50321i −0.0897596 + 0.155468i −0.907409 0.420248i \(-0.861943\pi\)
0.817650 + 0.575716i \(0.195277\pi\)
\(840\) −34.2342 + 38.8241i −1.18119 + 1.33956i
\(841\) −2.76099 4.78218i −0.0952066 0.164903i
\(842\) 9.97945 17.2849i 0.343914 0.595677i
\(843\) 16.2629 8.08836i 0.560125 0.278578i
\(844\) 36.6400 + 63.4624i 1.26120 + 2.18446i
\(845\) 4.37684 + 4.04931i 0.150568 + 0.139301i
\(846\) 41.0984 17.3496i 1.41299 0.596490i
\(847\) 9.36220 + 4.38052i 0.321689 + 0.150516i
\(848\) 21.5611 37.3449i 0.740411 1.28243i
\(849\) −1.20498 + 1.81663i −0.0413548 + 0.0623464i
\(850\) −20.3376 29.6446i −0.697574 1.01680i
\(851\) 4.71448i 0.161610i
\(852\) −9.69205 6.42880i −0.332044 0.220247i
\(853\) 13.8756 24.0332i 0.475091 0.822882i −0.524502 0.851409i \(-0.675748\pi\)
0.999593 + 0.0285270i \(0.00908167\pi\)
\(854\) −57.3698 + 4.94394i −1.96315 + 0.169178i
\(855\) 29.9967 25.2712i 1.02587 0.864255i
\(856\) 17.0077 + 29.4582i 0.581311 + 1.00686i
\(857\) −9.25825 + 5.34525i −0.316256 + 0.182590i −0.649722 0.760172i \(-0.725115\pi\)
0.333467 + 0.942762i \(0.391782\pi\)
\(858\) −32.6663 + 16.2466i −1.11521 + 0.554650i
\(859\) 4.59294 + 2.65174i 0.156709 + 0.0904761i 0.576304 0.817235i \(-0.304494\pi\)
−0.419595 + 0.907712i \(0.637828\pi\)
\(860\) −17.1133 + 18.4975i −0.583557 + 0.630758i
\(861\) 1.13863 + 47.6505i 0.0388044 + 1.62393i
\(862\) 25.0582 + 14.4674i 0.853486 + 0.492760i
\(863\) −1.67619 2.90325i −0.0570582 0.0988278i 0.836085 0.548599i \(-0.184839\pi\)
−0.893144 + 0.449772i \(0.851505\pi\)
\(864\) 2.70723 + 0.510050i 0.0921018 + 0.0173523i
\(865\) −38.6128 8.75420i −1.31288 0.297652i
\(866\) 34.2121 1.16257
\(867\) −14.6242 0.908939i −0.496662 0.0308692i
\(868\) −75.6233 + 6.51697i −2.56682 + 0.221200i
\(869\) 26.6341 15.3772i 0.903501 0.521636i
\(870\) −10.9111 44.8630i −0.369921 1.52100i
\(871\) −27.5516 + 15.9069i −0.933550 + 0.538985i
\(872\) 1.06158 1.83870i 0.0359495 0.0622663i
\(873\) 8.27137 + 1.03217i 0.279943 + 0.0349338i
\(874\) 36.7255i 1.24226i
\(875\) −24.6961 16.2820i −0.834880 0.550431i
\(876\) 24.8154 + 49.8952i 0.838434 + 1.68580i
\(877\) 35.2640 + 20.3597i 1.19078 + 0.687498i 0.958484 0.285146i \(-0.0920422\pi\)
0.232298 + 0.972645i \(0.425376\pi\)
\(878\) 40.2526i 1.35846i
\(879\) 1.06328 17.1074i 0.0358635 0.577018i
\(880\) 7.62208 + 24.5834i 0.256940 + 0.828708i
\(881\) −20.8315 −0.701831 −0.350916 0.936407i \(-0.614130\pi\)
−0.350916 + 0.936407i \(0.614130\pi\)
\(882\) −27.9410 43.4597i −0.940823 1.46336i
\(883\) 28.9816i 0.975309i 0.873037 + 0.487655i \(0.162147\pi\)
−0.873037 + 0.487655i \(0.837853\pi\)
\(884\) 38.0764i 1.28065i
\(885\) −17.2306 18.0501i −0.579201 0.606747i
\(886\) −36.6819 −1.23235
\(887\) −5.52226 3.18828i −0.185419 0.107052i 0.404417 0.914575i \(-0.367474\pi\)
−0.589836 + 0.807523i \(0.700808\pi\)
\(888\) −1.00229 + 16.1261i −0.0336347 + 0.541157i
\(889\) 33.2727 2.86734i 1.11593 0.0961673i
\(890\) 37.1023 11.5035i 1.24367 0.385600i
\(891\) −5.89059 + 23.2347i −0.197342 + 0.778393i
\(892\) −18.0521 + 31.2671i −0.604428 + 1.04690i
\(893\) −17.6696 30.6046i −0.591290 1.02414i
\(894\) −40.0391 + 19.9135i −1.33911 + 0.666006i
\(895\) 8.86460 9.58161i 0.296311 0.320278i
\(896\) −4.34268 50.3927i −0.145079 1.68350i
\(897\) 7.85709 11.8453i 0.262340 0.395505i
\(898\) 46.7673i 1.56064i
\(899\) 17.1483 29.7016i 0.571926 0.990605i
\(900\) −2.82271 + 60.7319i −0.0940904 + 2.02440i
\(901\) −25.2525 + 14.5795i −0.841283 + 0.485715i
\(902\) 59.0236 + 34.0773i 1.96527 + 1.13465i
\(903\) −6.63258 10.8792i −0.220718 0.362037i
\(904\) −26.0098 45.0503i −0.865073 1.49835i
\(905\) −28.6972 6.50615i −0.953927 0.216272i
\(906\) 103.631 + 6.44102i 3.44292 + 0.213989i
\(907\) 7.23234 4.17559i 0.240146 0.138648i −0.375098 0.926985i \(-0.622391\pi\)
0.615244 + 0.788337i \(0.289058\pi\)
\(908\) −52.1948 + 30.1347i −1.73215 + 1.00006i
\(909\) 24.0965 31.8461i 0.799229 1.05627i
\(910\) −17.6422 43.3359i −0.584832 1.43657i
\(911\) −1.18966 0.686853i −0.0394153 0.0227565i 0.480163 0.877179i \(-0.340578\pi\)
−0.519578 + 0.854423i \(0.673911\pi\)
\(912\) 2.71511 43.6841i 0.0899063 1.44653i
\(913\) 37.6621 1.24643
\(914\) 83.0226i 2.74614i
\(915\) −24.7819 + 23.6568i −0.819265 + 0.782071i
\(916\) −53.3983 30.8295i −1.76433 1.01864i
\(917\) 45.4057 + 21.2450i 1.49943 + 0.701573i
\(918\) −28.3372 24.3478i −0.935268 0.803596i
\(919\) −11.9247 20.6542i −0.393360 0.681319i 0.599530 0.800352i \(-0.295354\pi\)
−0.992890 + 0.119033i \(0.962021\pi\)
\(920\) −21.1671 19.5831i −0.697859 0.645637i
\(921\) −11.3046 + 17.0427i −0.372498 + 0.561578i
\(922\) −38.0819 + 65.9599i −1.25416 + 2.17227i
\(923\) 4.61201 2.66275i 0.151806 0.0876454i
\(924\) −49.4541 + 1.18173i −1.62692 + 0.0388760i
\(925\) −9.20552 + 0.716731i −0.302676 + 0.0235660i
\(926\) −54.5813 + 31.5125i −1.79365 + 1.03557i
\(927\) −5.13369 0.640627i −0.168613 0.0210409i
\(928\) −2.22474 1.28445i −0.0730306 0.0421642i
\(929\) 2.64891 0.0869080 0.0434540 0.999055i \(-0.486164\pi\)
0.0434540 + 0.999055i \(0.486164\pi\)
\(930\) −48.7861 + 46.5712i −1.59976 + 1.52713i
\(931\) −31.4219 + 26.2269i −1.02981 + 0.859553i
\(932\) −19.9336 34.5261i −0.652948 1.13094i
\(933\) 5.56430 8.38874i 0.182167 0.274635i
\(934\) −50.0191 + 28.8786i −1.63668 + 0.944936i
\(935\) 3.84811 16.9732i 0.125847 0.555082i
\(936\) −29.3939 + 38.8472i −0.960768 + 1.26976i
\(937\) 41.6720 1.36136 0.680682 0.732579i \(-0.261684\pi\)
0.680682 + 0.732579i \(0.261684\pi\)
\(938\) −64.1842 + 5.53118i −2.09569 + 0.180599i
\(939\) 31.1207 46.9176i 1.01559 1.53110i
\(940\) 53.4218 + 12.1116i 1.74243 + 0.395038i
\(941\) 21.9989 0.717142 0.358571 0.933502i \(-0.383264\pi\)
0.358571 + 0.933502i \(0.383264\pi\)
\(942\) −1.97732 + 2.98100i −0.0644244 + 0.0971263i
\(943\) −26.5537 −0.864707
\(944\) −27.8458 −0.906305
\(945\) −29.1492 9.76350i −0.948223 0.317607i
\(946\) −18.2191 −0.592355
\(947\) 23.1432 0.752054 0.376027 0.926609i \(-0.377290\pi\)
0.376027 + 0.926609i \(0.377290\pi\)
\(948\) 44.8102 67.5559i 1.45537 2.19411i
\(949\) −25.5165 −0.828301
\(950\) 71.7104 5.58329i 2.32659 0.181146i
\(951\) 12.4538 18.7754i 0.403844 0.608835i
\(952\) 16.5525 35.3766i 0.536469 1.14656i
\(953\) −15.4692 −0.501097 −0.250549 0.968104i \(-0.580611\pi\)
−0.250549 + 0.968104i \(0.580611\pi\)
\(954\) 73.0787 + 9.11939i 2.36601 + 0.295251i
\(955\) −1.53951 0.349033i −0.0498173 0.0112944i
\(956\) −3.60668 + 2.08232i −0.116648 + 0.0673469i
\(957\) 12.3552 18.6267i 0.399387 0.602116i
\(958\) −25.6480 44.4236i −0.828649 1.43526i
\(959\) −20.7714 + 14.5040i −0.670745 + 0.468360i
\(960\) −19.6272 20.5607i −0.633466 0.663592i
\(961\) −19.1001 −0.616131
\(962\) −12.6484 7.30254i −0.407800 0.235443i
\(963\) −12.1893 + 16.1095i −0.392796 + 0.519122i
\(964\) −5.14787 + 2.97213i −0.165802 + 0.0957257i
\(965\) 42.8174 + 9.70744i 1.37834 + 0.312494i
\(966\) 24.5763 14.9831i 0.790731 0.482074i
\(967\) −32.8410 + 18.9608i −1.05610 + 0.609737i −0.924350 0.381546i \(-0.875392\pi\)
−0.131746 + 0.991283i \(0.542058\pi\)
\(968\) 9.86740 17.0908i 0.317150 0.549320i
\(969\) −16.3595 + 24.6636i −0.525544 + 0.792310i
\(970\) 11.2203 + 10.3807i 0.360264 + 0.333304i
\(971\) −13.5099 23.3998i −0.433553 0.750936i 0.563623 0.826032i \(-0.309407\pi\)
−0.997176 + 0.0750961i \(0.976074\pi\)
\(972\) 13.3707 + 61.7517i 0.428864 + 1.98069i
\(973\) −1.56039 2.23466i −0.0500239 0.0716398i
\(974\) −6.07457 3.50715i −0.194642 0.112376i
\(975\) −24.3238 13.5410i −0.778985 0.433658i
\(976\) 38.2310i 1.22375i
\(977\) 20.8740 0.667820 0.333910 0.942605i \(-0.391632\pi\)
0.333910 + 0.942605i \(0.391632\pi\)
\(978\) −1.45997 + 23.4899i −0.0466848 + 0.751124i
\(979\) 16.2858 + 9.40260i 0.520496 + 0.300508i
\(980\) 3.23539 63.3595i 0.103351 2.02395i
\(981\) 1.25121 + 0.156137i 0.0399482 + 0.00498508i
\(982\) 5.58743 3.22590i 0.178302 0.102943i
\(983\) 26.9799 15.5768i 0.860525 0.496824i −0.00366333 0.999993i \(-0.501166\pi\)
0.864188 + 0.503169i \(0.167833\pi\)
\(984\) 90.8282 + 5.64527i 2.89550 + 0.179965i
\(985\) −5.79674 + 25.5682i −0.184700 + 0.814669i
\(986\) 17.4194 + 30.1712i 0.554746 + 0.960847i
\(987\) −13.2715 + 24.3103i −0.422438 + 0.773805i
\(988\) 65.9751 + 38.0907i 2.09895 + 1.21183i
\(989\) 6.14735 3.54917i 0.195474 0.112857i
\(990\) −33.6166 + 28.3208i −1.06841 + 0.900093i
\(991\) 11.1945 19.3895i 0.355606 0.615928i −0.631615 0.775282i \(-0.717608\pi\)
0.987222 + 0.159354i \(0.0509411\pi\)
\(992\) 3.75264i 0.119146i
\(993\) 0.169498 0.255535i 0.00537885 0.00810916i
\(994\) 10.7441 0.925895i 0.340784 0.0293676i
\(995\) 4.23698 4.57969i 0.134321 0.145186i
\(996\) 88.8878 44.2084i 2.81652 1.40080i
\(997\) 26.2342 + 45.4390i 0.830847 + 1.43907i 0.897368 + 0.441284i \(0.145477\pi\)
−0.0665210 + 0.997785i \(0.521190\pi\)
\(998\) 27.6164 47.8331i 0.874183 1.51413i
\(999\) −9.05467 + 3.17629i −0.286477 + 0.100493i
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 315.2.bq.a.164.4 yes 88
3.2 odd 2 945.2.bq.a.899.41 88
5.4 even 2 inner 315.2.bq.a.164.41 yes 88
7.5 odd 6 315.2.u.a.299.41 yes 88
9.4 even 3 945.2.u.a.584.41 88
9.5 odd 6 315.2.u.a.59.4 88
15.14 odd 2 945.2.bq.a.899.4 88
21.5 even 6 945.2.u.a.89.4 88
35.19 odd 6 315.2.u.a.299.4 yes 88
45.4 even 6 945.2.u.a.584.4 88
45.14 odd 6 315.2.u.a.59.41 yes 88
63.5 even 6 inner 315.2.bq.a.194.41 yes 88
63.40 odd 6 945.2.bq.a.719.4 88
105.89 even 6 945.2.u.a.89.41 88
315.194 even 6 inner 315.2.bq.a.194.4 yes 88
315.229 odd 6 945.2.bq.a.719.41 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.u.a.59.4 88 9.5 odd 6
315.2.u.a.59.41 yes 88 45.14 odd 6
315.2.u.a.299.4 yes 88 35.19 odd 6
315.2.u.a.299.41 yes 88 7.5 odd 6
315.2.bq.a.164.4 yes 88 1.1 even 1 trivial
315.2.bq.a.164.41 yes 88 5.4 even 2 inner
315.2.bq.a.194.4 yes 88 315.194 even 6 inner
315.2.bq.a.194.41 yes 88 63.5 even 6 inner
945.2.u.a.89.4 88 21.5 even 6
945.2.u.a.89.41 88 105.89 even 6
945.2.u.a.584.4 88 45.4 even 6
945.2.u.a.584.41 88 9.4 even 3
945.2.bq.a.719.4 88 63.40 odd 6
945.2.bq.a.719.41 88 315.229 odd 6
945.2.bq.a.899.4 88 15.14 odd 2
945.2.bq.a.899.41 88 3.2 odd 2