Properties

Label 930.2.o.d.161.15
Level $930$
Weight $2$
Character 930.161
Analytic conductor $7.426$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(161,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 161.15
Character \(\chi\) \(=\) 930.161
Dual form 930.2.o.d.491.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.645214 + 1.60739i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.60739 + 0.645214i) q^{6} +(-2.35643 - 4.08145i) q^{7} -1.00000i q^{8} +(-2.16740 + 2.07422i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.645214 + 1.60739i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.60739 + 0.645214i) q^{6} +(-2.35643 - 4.08145i) q^{7} -1.00000i q^{8} +(-2.16740 + 2.07422i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-3.18522 + 5.51697i) q^{11} +(-0.645214 - 1.60739i) q^{12} +(-2.96986 - 1.71465i) q^{13} +(4.08145 - 2.35643i) q^{14} +(-0.244922 + 1.71465i) q^{15} +1.00000 q^{16} +(-1.65822 - 2.87212i) q^{17} +(-2.07422 - 2.16740i) q^{18} +(-2.56125 - 4.43621i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(5.04008 - 6.42110i) q^{21} +(-5.51697 - 3.18522i) q^{22} +4.89435 q^{23} +(1.60739 - 0.645214i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.71465 - 2.96986i) q^{26} +(-4.73251 - 2.14553i) q^{27} +(2.35643 + 4.08145i) q^{28} -5.57108 q^{29} +(-1.71465 - 0.244922i) q^{30} +(3.67202 + 4.18524i) q^{31} +1.00000i q^{32} +(-10.9231 - 1.56027i) q^{33} +(2.87212 - 1.65822i) q^{34} -4.71285i q^{35} +(2.16740 - 2.07422i) q^{36} +(-4.26827 + 2.46429i) q^{37} +(4.43621 - 2.56125i) q^{38} +(0.839911 - 5.88003i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-8.33642 - 4.81303i) q^{41} +(6.42110 + 5.04008i) q^{42} +(-5.26899 + 3.04205i) q^{43} +(3.18522 - 5.51697i) q^{44} +(-2.91413 + 0.712629i) q^{45} +4.89435i q^{46} +3.50612i q^{47} +(0.645214 + 1.60739i) q^{48} +(-7.60549 + 13.1731i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.54671 - 4.51854i) q^{51} +(2.96986 + 1.71465i) q^{52} +(-0.645608 + 1.11823i) q^{53} +(2.14553 - 4.73251i) q^{54} +(-5.51697 + 3.18522i) q^{55} +(-4.08145 + 2.35643i) q^{56} +(5.47816 - 6.97923i) q^{57} -5.57108i q^{58} +(4.87072 - 2.81211i) q^{59} +(0.244922 - 1.71465i) q^{60} -1.31888i q^{61} +(-4.18524 + 3.67202i) q^{62} +(13.5731 + 3.95837i) q^{63} -1.00000 q^{64} +(-1.71465 - 2.96986i) q^{65} +(1.56027 - 10.9231i) q^{66} +(7.24848 - 12.5547i) q^{67} +(1.65822 + 2.87212i) q^{68} +(3.15791 + 7.86713i) q^{69} +4.71285 q^{70} +(1.61036 + 0.929740i) q^{71} +(2.07422 + 2.16740i) q^{72} +(9.05398 + 5.22732i) q^{73} +(-2.46429 - 4.26827i) q^{74} +(-1.06943 + 1.36247i) q^{75} +(2.56125 + 4.43621i) q^{76} +30.0230 q^{77} +(5.88003 + 0.839911i) q^{78} +(0.954760 - 0.551231i) q^{79} +(0.866025 + 0.500000i) q^{80} +(0.395219 - 8.99132i) q^{81} +(4.81303 - 8.33642i) q^{82} +(-3.19991 + 5.54241i) q^{83} +(-5.04008 + 6.42110i) q^{84} -3.31644i q^{85} +(-3.04205 - 5.26899i) q^{86} +(-3.59454 - 8.95489i) q^{87} +(5.51697 + 3.18522i) q^{88} -6.30402 q^{89} +(-0.712629 - 2.91413i) q^{90} +16.1618i q^{91} -4.89435 q^{92} +(-4.35807 + 8.60275i) q^{93} -3.50612 q^{94} -5.12249i q^{95} +(-1.60739 + 0.645214i) q^{96} +0.469167 q^{97} +(-13.1731 - 7.60549i) q^{98} +(-4.53977 - 18.5643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.645214 + 1.60739i 0.372515 + 0.928026i
\(4\) −1.00000 −0.500000
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) −1.60739 + 0.645214i −0.656214 + 0.263408i
\(7\) −2.35643 4.08145i −0.890645 1.54264i −0.839103 0.543972i \(-0.816920\pi\)
−0.0515421 0.998671i \(-0.516414\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.16740 + 2.07422i −0.722466 + 0.691407i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −3.18522 + 5.51697i −0.960381 + 1.66343i −0.238838 + 0.971060i \(0.576766\pi\)
−0.721543 + 0.692369i \(0.756567\pi\)
\(12\) −0.645214 1.60739i −0.186257 0.464013i
\(13\) −2.96986 1.71465i −0.823690 0.475557i 0.0279975 0.999608i \(-0.491087\pi\)
−0.851687 + 0.524051i \(0.824420\pi\)
\(14\) 4.08145 2.35643i 1.09081 0.629781i
\(15\) −0.244922 + 1.71465i −0.0632387 + 0.442720i
\(16\) 1.00000 0.250000
\(17\) −1.65822 2.87212i −0.402177 0.696592i 0.591811 0.806077i \(-0.298413\pi\)
−0.993988 + 0.109485i \(0.965080\pi\)
\(18\) −2.07422 2.16740i −0.488898 0.510860i
\(19\) −2.56125 4.43621i −0.587590 1.01774i −0.994547 0.104289i \(-0.966743\pi\)
0.406957 0.913447i \(-0.366590\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 5.04008 6.42110i 1.09983 1.40120i
\(22\) −5.51697 3.18522i −1.17622 0.679092i
\(23\) 4.89435 1.02054 0.510271 0.860013i \(-0.329545\pi\)
0.510271 + 0.860013i \(0.329545\pi\)
\(24\) 1.60739 0.645214i 0.328107 0.131704i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.71465 2.96986i 0.336270 0.582436i
\(27\) −4.73251 2.14553i −0.910773 0.412908i
\(28\) 2.35643 + 4.08145i 0.445323 + 0.771322i
\(29\) −5.57108 −1.03452 −0.517262 0.855827i \(-0.673049\pi\)
−0.517262 + 0.855827i \(0.673049\pi\)
\(30\) −1.71465 0.244922i −0.313050 0.0447165i
\(31\) 3.67202 + 4.18524i 0.659515 + 0.751692i
\(32\) 1.00000i 0.176777i
\(33\) −10.9231 1.56027i −1.90146 0.271607i
\(34\) 2.87212 1.65822i 0.492565 0.284382i
\(35\) 4.71285i 0.796617i
\(36\) 2.16740 2.07422i 0.361233 0.345703i
\(37\) −4.26827 + 2.46429i −0.701699 + 0.405126i −0.807980 0.589210i \(-0.799439\pi\)
0.106281 + 0.994336i \(0.466106\pi\)
\(38\) 4.43621 2.56125i 0.719648 0.415489i
\(39\) 0.839911 5.88003i 0.134493 0.941558i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −8.33642 4.81303i −1.30193 0.751670i −0.321195 0.947013i \(-0.604085\pi\)
−0.980735 + 0.195343i \(0.937418\pi\)
\(42\) 6.42110 + 5.04008i 0.990798 + 0.777701i
\(43\) −5.26899 + 3.04205i −0.803514 + 0.463909i −0.844698 0.535243i \(-0.820220\pi\)
0.0411847 + 0.999152i \(0.486887\pi\)
\(44\) 3.18522 5.51697i 0.480191 0.831714i
\(45\) −2.91413 + 0.712629i −0.434413 + 0.106232i
\(46\) 4.89435i 0.721633i
\(47\) 3.50612i 0.511421i 0.966753 + 0.255710i \(0.0823094\pi\)
−0.966753 + 0.255710i \(0.917691\pi\)
\(48\) 0.645214 + 1.60739i 0.0931287 + 0.232007i
\(49\) −7.60549 + 13.1731i −1.08650 + 1.88187i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 3.54671 4.51854i 0.496639 0.632722i
\(52\) 2.96986 + 1.71465i 0.411845 + 0.237779i
\(53\) −0.645608 + 1.11823i −0.0886810 + 0.153600i −0.906954 0.421230i \(-0.861599\pi\)
0.818273 + 0.574830i \(0.194932\pi\)
\(54\) 2.14553 4.73251i 0.291970 0.644014i
\(55\) −5.51697 + 3.18522i −0.743908 + 0.429495i
\(56\) −4.08145 + 2.35643i −0.545407 + 0.314891i
\(57\) 5.47816 6.97923i 0.725600 0.924421i
\(58\) 5.57108i 0.731519i
\(59\) 4.87072 2.81211i 0.634114 0.366106i −0.148229 0.988953i \(-0.547357\pi\)
0.782344 + 0.622847i \(0.214024\pi\)
\(60\) 0.244922 1.71465i 0.0316193 0.221360i
\(61\) 1.31888i 0.168866i −0.996429 0.0844328i \(-0.973092\pi\)
0.996429 0.0844328i \(-0.0269078\pi\)
\(62\) −4.18524 + 3.67202i −0.531526 + 0.466347i
\(63\) 13.5731 + 3.95837i 1.71005 + 0.498708i
\(64\) −1.00000 −0.125000
\(65\) −1.71465 2.96986i −0.212676 0.368365i
\(66\) 1.56027 10.9231i 0.192055 1.34454i
\(67\) 7.24848 12.5547i 0.885542 1.53380i 0.0404514 0.999182i \(-0.487120\pi\)
0.845091 0.534623i \(-0.179546\pi\)
\(68\) 1.65822 + 2.87212i 0.201089 + 0.348296i
\(69\) 3.15791 + 7.86713i 0.380167 + 0.947091i
\(70\) 4.71285 0.563294
\(71\) 1.61036 + 0.929740i 0.191114 + 0.110340i 0.592504 0.805567i \(-0.298139\pi\)
−0.401390 + 0.915907i \(0.631473\pi\)
\(72\) 2.07422 + 2.16740i 0.244449 + 0.255430i
\(73\) 9.05398 + 5.22732i 1.05969 + 0.611811i 0.925346 0.379124i \(-0.123774\pi\)
0.134342 + 0.990935i \(0.457108\pi\)
\(74\) −2.46429 4.26827i −0.286467 0.496176i
\(75\) −1.06943 + 1.36247i −0.123487 + 0.157324i
\(76\) 2.56125 + 4.43621i 0.293795 + 0.508868i
\(77\) 30.0230 3.42144
\(78\) 5.88003 + 0.839911i 0.665782 + 0.0951012i
\(79\) 0.954760 0.551231i 0.107419 0.0620183i −0.445328 0.895367i \(-0.646913\pi\)
0.552747 + 0.833349i \(0.313580\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 0.395219 8.99132i 0.0439133 0.999035i
\(82\) 4.81303 8.33642i 0.531511 0.920603i
\(83\) −3.19991 + 5.54241i −0.351236 + 0.608358i −0.986466 0.163964i \(-0.947572\pi\)
0.635231 + 0.772323i \(0.280905\pi\)
\(84\) −5.04008 + 6.42110i −0.549917 + 0.700600i
\(85\) 3.31644i 0.359718i
\(86\) −3.04205 5.26899i −0.328033 0.568170i
\(87\) −3.59454 8.95489i −0.385375 0.960065i
\(88\) 5.51697 + 3.18522i 0.588111 + 0.339546i
\(89\) −6.30402 −0.668225 −0.334112 0.942533i \(-0.608437\pi\)
−0.334112 + 0.942533i \(0.608437\pi\)
\(90\) −0.712629 2.91413i −0.0751177 0.307176i
\(91\) 16.1618i 1.69421i
\(92\) −4.89435 −0.510271
\(93\) −4.35807 + 8.60275i −0.451911 + 0.892063i
\(94\) −3.50612 −0.361629
\(95\) 5.12249i 0.525557i
\(96\) −1.60739 + 0.645214i −0.164053 + 0.0658519i
\(97\) 0.469167 0.0476367 0.0238183 0.999716i \(-0.492418\pi\)
0.0238183 + 0.999716i \(0.492418\pi\)
\(98\) −13.1731 7.60549i −1.33068 0.768270i
\(99\) −4.53977 18.5643i −0.456264 1.86578i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 15.8938i 1.58149i 0.612143 + 0.790747i \(0.290308\pi\)
−0.612143 + 0.790747i \(0.709692\pi\)
\(102\) 4.51854 + 3.54671i 0.447402 + 0.351176i
\(103\) −7.58503 + 13.1377i −0.747375 + 1.29449i 0.201701 + 0.979447i \(0.435353\pi\)
−0.949077 + 0.315045i \(0.897980\pi\)
\(104\) −1.71465 + 2.96986i −0.168135 + 0.291218i
\(105\) 7.57539 3.04080i 0.739282 0.296752i
\(106\) −1.11823 0.645608i −0.108612 0.0627070i
\(107\) 12.6046 7.27724i 1.21853 0.703518i 0.253925 0.967224i \(-0.418278\pi\)
0.964603 + 0.263706i \(0.0849449\pi\)
\(108\) 4.73251 + 2.14553i 0.455386 + 0.206454i
\(109\) −13.1729 −1.26174 −0.630869 0.775890i \(-0.717301\pi\)
−0.630869 + 0.775890i \(0.717301\pi\)
\(110\) −3.18522 5.51697i −0.303699 0.526022i
\(111\) −6.71501 5.27077i −0.637361 0.500280i
\(112\) −2.35643 4.08145i −0.222661 0.385661i
\(113\) 3.12246 + 1.80276i 0.293737 + 0.169589i 0.639626 0.768686i \(-0.279089\pi\)
−0.345889 + 0.938275i \(0.612423\pi\)
\(114\) 6.97923 + 5.47816i 0.653664 + 0.513077i
\(115\) 4.23863 + 2.44718i 0.395255 + 0.228200i
\(116\) 5.57108 0.517262
\(117\) 9.99341 2.44381i 0.923891 0.225931i
\(118\) 2.81211 + 4.87072i 0.258876 + 0.448386i
\(119\) −7.81495 + 13.5359i −0.716395 + 1.24083i
\(120\) 1.71465 + 0.244922i 0.156525 + 0.0223583i
\(121\) −14.7913 25.6193i −1.34466 2.32903i
\(122\) 1.31888 0.119406
\(123\) 2.35764 16.5053i 0.212581 1.48823i
\(124\) −3.67202 4.18524i −0.329757 0.375846i
\(125\) 1.00000i 0.0894427i
\(126\) −3.95837 + 13.5731i −0.352640 + 1.20919i
\(127\) 2.83079 1.63436i 0.251192 0.145026i −0.369118 0.929383i \(-0.620340\pi\)
0.620310 + 0.784357i \(0.287007\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −8.28939 6.50654i −0.729840 0.572869i
\(130\) 2.96986 1.71465i 0.260474 0.150384i
\(131\) −8.11286 + 4.68396i −0.708824 + 0.409240i −0.810625 0.585565i \(-0.800873\pi\)
0.101802 + 0.994805i \(0.467539\pi\)
\(132\) 10.9231 + 1.56027i 0.950731 + 0.135804i
\(133\) −12.0708 + 20.9072i −1.04667 + 1.81288i
\(134\) 12.5547 + 7.24848i 1.08456 + 0.626173i
\(135\) −3.02571 4.22434i −0.260412 0.363574i
\(136\) −2.87212 + 1.65822i −0.246282 + 0.142191i
\(137\) −2.06547 + 3.57749i −0.176465 + 0.305646i −0.940667 0.339331i \(-0.889799\pi\)
0.764203 + 0.644976i \(0.223133\pi\)
\(138\) −7.86713 + 3.15791i −0.669694 + 0.268819i
\(139\) 20.7544i 1.76037i 0.474633 + 0.880184i \(0.342581\pi\)
−0.474633 + 0.880184i \(0.657419\pi\)
\(140\) 4.71285i 0.398309i
\(141\) −5.63571 + 2.26220i −0.474612 + 0.190512i
\(142\) −0.929740 + 1.61036i −0.0780220 + 0.135138i
\(143\) 18.9193 10.9231i 1.58211 0.913433i
\(144\) −2.16740 + 2.07422i −0.180616 + 0.172852i
\(145\) −4.82470 2.78554i −0.400669 0.231326i
\(146\) −5.22732 + 9.05398i −0.432616 + 0.749313i
\(147\) −26.0814 3.72551i −2.15116 0.307275i
\(148\) 4.26827 2.46429i 0.350849 0.202563i
\(149\) 0.0549861 0.0317462i 0.00450464 0.00260075i −0.497746 0.867323i \(-0.665839\pi\)
0.502251 + 0.864722i \(0.332505\pi\)
\(150\) −1.36247 1.06943i −0.111245 0.0873188i
\(151\) 2.80211i 0.228033i −0.993479 0.114016i \(-0.963628\pi\)
0.993479 0.114016i \(-0.0363717\pi\)
\(152\) −4.43621 + 2.56125i −0.359824 + 0.207745i
\(153\) 9.55144 + 2.78551i 0.772188 + 0.225195i
\(154\) 30.0230i 2.41932i
\(155\) 1.08744 + 5.46054i 0.0873456 + 0.438601i
\(156\) −0.839911 + 5.88003i −0.0672467 + 0.470779i
\(157\) 0.873360 0.0697017 0.0348509 0.999393i \(-0.488904\pi\)
0.0348509 + 0.999393i \(0.488904\pi\)
\(158\) 0.551231 + 0.954760i 0.0438536 + 0.0759566i
\(159\) −2.21398 0.316248i −0.175580 0.0250801i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −11.5332 19.9761i −0.908942 1.57433i
\(162\) 8.99132 + 0.395219i 0.706425 + 0.0310514i
\(163\) 2.46179 0.192822 0.0964112 0.995342i \(-0.469264\pi\)
0.0964112 + 0.995342i \(0.469264\pi\)
\(164\) 8.33642 + 4.81303i 0.650965 + 0.375835i
\(165\) −8.67952 6.81276i −0.675700 0.530373i
\(166\) −5.54241 3.19991i −0.430174 0.248361i
\(167\) 6.58051 + 11.3978i 0.509215 + 0.881987i 0.999943 + 0.0106739i \(0.00339766\pi\)
−0.490728 + 0.871313i \(0.663269\pi\)
\(168\) −6.42110 5.04008i −0.495399 0.388850i
\(169\) −0.619974 1.07383i −0.0476903 0.0826020i
\(170\) 3.31644 0.254359
\(171\) 14.7529 + 4.30244i 1.12818 + 0.329016i
\(172\) 5.26899 3.04205i 0.401757 0.231954i
\(173\) −2.37379 1.37051i −0.180476 0.104198i 0.407040 0.913410i \(-0.366561\pi\)
−0.587516 + 0.809212i \(0.699894\pi\)
\(174\) 8.95489 3.59454i 0.678868 0.272501i
\(175\) 2.35643 4.08145i 0.178129 0.308529i
\(176\) −3.18522 + 5.51697i −0.240095 + 0.415857i
\(177\) 7.66282 + 6.01473i 0.575973 + 0.452095i
\(178\) 6.30402i 0.472506i
\(179\) 1.52614 + 2.64335i 0.114069 + 0.197573i 0.917407 0.397950i \(-0.130278\pi\)
−0.803338 + 0.595523i \(0.796945\pi\)
\(180\) 2.91413 0.712629i 0.217207 0.0531162i
\(181\) −13.9592 8.05934i −1.03758 0.599046i −0.118432 0.992962i \(-0.537787\pi\)
−0.919146 + 0.393916i \(0.871120\pi\)
\(182\) −16.1618 −1.19799
\(183\) 2.11996 0.850962i 0.156712 0.0629049i
\(184\) 4.89435i 0.360816i
\(185\) −4.92857 −0.362356
\(186\) −8.60275 4.35807i −0.630784 0.319549i
\(187\) 21.1272 1.54497
\(188\) 3.50612i 0.255710i
\(189\) 2.39494 + 24.3713i 0.174206 + 1.77275i
\(190\) 5.12249 0.371625
\(191\) 7.57495 + 4.37340i 0.548104 + 0.316448i 0.748357 0.663296i \(-0.230843\pi\)
−0.200253 + 0.979744i \(0.564176\pi\)
\(192\) −0.645214 1.60739i −0.0465643 0.116003i
\(193\) −10.7607 18.6381i −0.774574 1.34160i −0.935033 0.354560i \(-0.884631\pi\)
0.160459 0.987043i \(-0.448703\pi\)
\(194\) 0.469167i 0.0336842i
\(195\) 3.66740 4.67230i 0.262628 0.334590i
\(196\) 7.60549 13.1731i 0.543249 0.940935i
\(197\) −7.08814 + 12.2770i −0.505009 + 0.874701i 0.494974 + 0.868908i \(0.335177\pi\)
−0.999983 + 0.00579339i \(0.998156\pi\)
\(198\) 18.5643 4.53977i 1.31931 0.322627i
\(199\) −6.70999 3.87401i −0.475658 0.274622i 0.242947 0.970040i \(-0.421886\pi\)
−0.718605 + 0.695418i \(0.755219\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) 24.8571 + 3.55063i 1.75329 + 0.250442i
\(202\) −15.8938 −1.11828
\(203\) 13.1278 + 22.7381i 0.921394 + 1.59590i
\(204\) −3.54671 + 4.51854i −0.248319 + 0.316361i
\(205\) −4.81303 8.33642i −0.336157 0.582241i
\(206\) −13.1377 7.58503i −0.915344 0.528474i
\(207\) −10.6080 + 10.1520i −0.737307 + 0.705610i
\(208\) −2.96986 1.71465i −0.205922 0.118889i
\(209\) 32.6326 2.25724
\(210\) 3.04080 + 7.57539i 0.209835 + 0.522751i
\(211\) −7.68821 13.3164i −0.529279 0.916737i −0.999417 0.0341446i \(-0.989129\pi\)
0.470138 0.882593i \(-0.344204\pi\)
\(212\) 0.645608 1.11823i 0.0443405 0.0768000i
\(213\) −0.455428 + 3.18835i −0.0312054 + 0.218462i
\(214\) 7.27724 + 12.6046i 0.497462 + 0.861630i
\(215\) −6.08411 −0.414933
\(216\) −2.14553 + 4.73251i −0.145985 + 0.322007i
\(217\) 8.42900 24.8494i 0.572198 1.68689i
\(218\) 13.1729i 0.892183i
\(219\) −2.56057 + 17.9260i −0.173028 + 1.21133i
\(220\) 5.51697 3.18522i 0.371954 0.214748i
\(221\) 11.3730i 0.765034i
\(222\) 5.27077 6.71501i 0.353751 0.450682i
\(223\) −9.74718 + 5.62754i −0.652719 + 0.376848i −0.789497 0.613754i \(-0.789659\pi\)
0.136778 + 0.990602i \(0.456325\pi\)
\(224\) 4.08145 2.35643i 0.272703 0.157445i
\(225\) −2.88003 0.839911i −0.192002 0.0559940i
\(226\) −1.80276 + 3.12246i −0.119918 + 0.207703i
\(227\) −19.1006 11.0278i −1.26775 0.731938i −0.293191 0.956054i \(-0.594717\pi\)
−0.974562 + 0.224116i \(0.928050\pi\)
\(228\) −5.47816 + 6.97923i −0.362800 + 0.462210i
\(229\) −6.32764 + 3.65326i −0.418142 + 0.241414i −0.694282 0.719703i \(-0.744278\pi\)
0.276140 + 0.961117i \(0.410945\pi\)
\(230\) −2.44718 + 4.23863i −0.161362 + 0.279487i
\(231\) 19.3713 + 48.2586i 1.27453 + 3.17518i
\(232\) 5.57108i 0.365759i
\(233\) 9.29519i 0.608948i 0.952521 + 0.304474i \(0.0984806\pi\)
−0.952521 + 0.304474i \(0.901519\pi\)
\(234\) 2.44381 + 9.99341i 0.159757 + 0.653290i
\(235\) −1.75306 + 3.03639i −0.114357 + 0.198072i
\(236\) −4.87072 + 2.81211i −0.317057 + 0.183053i
\(237\) 1.50207 + 1.17901i 0.0975698 + 0.0765848i
\(238\) −13.5359 7.81495i −0.877401 0.506568i
\(239\) 12.0377 20.8498i 0.778651 1.34866i −0.154068 0.988060i \(-0.549238\pi\)
0.932719 0.360603i \(-0.117429\pi\)
\(240\) −0.244922 + 1.71465i −0.0158097 + 0.110680i
\(241\) −9.91581 + 5.72490i −0.638733 + 0.368773i −0.784126 0.620601i \(-0.786889\pi\)
0.145393 + 0.989374i \(0.453555\pi\)
\(242\) 25.6193 14.7913i 1.64687 0.950821i
\(243\) 14.7075 5.16606i 0.943489 0.331403i
\(244\) 1.31888i 0.0844328i
\(245\) −13.1731 + 7.60549i −0.841598 + 0.485897i
\(246\) 16.5053 + 2.35764i 1.05234 + 0.150318i
\(247\) 17.5665i 1.11773i
\(248\) 4.18524 3.67202i 0.265763 0.233174i
\(249\) −10.9734 1.56746i −0.695413 0.0993337i
\(250\) −1.00000 −0.0632456
\(251\) 11.2082 + 19.4132i 0.707457 + 1.22535i 0.965797 + 0.259298i \(0.0834912\pi\)
−0.258340 + 0.966054i \(0.583175\pi\)
\(252\) −13.5731 3.95837i −0.855027 0.249354i
\(253\) −15.5896 + 27.0020i −0.980110 + 1.69760i
\(254\) 1.63436 + 2.83079i 0.102549 + 0.177620i
\(255\) 5.33081 2.13981i 0.333828 0.134000i
\(256\) 1.00000 0.0625000
\(257\) −27.5281 15.8934i −1.71716 0.991401i −0.924007 0.382376i \(-0.875106\pi\)
−0.793151 0.609025i \(-0.791561\pi\)
\(258\) 6.50654 8.28939i 0.405080 0.516075i
\(259\) 20.1157 + 11.6138i 1.24993 + 0.721647i
\(260\) 1.71465 + 2.96986i 0.106338 + 0.184183i
\(261\) 12.0747 11.5556i 0.747408 0.715277i
\(262\) −4.68396 8.11286i −0.289376 0.501214i
\(263\) −8.90216 −0.548931 −0.274465 0.961597i \(-0.588501\pi\)
−0.274465 + 0.961597i \(0.588501\pi\)
\(264\) −1.56027 + 10.9231i −0.0960277 + 0.672268i
\(265\) −1.11823 + 0.645608i −0.0686920 + 0.0396594i
\(266\) −20.9072 12.0708i −1.28190 0.740107i
\(267\) −4.06744 10.1330i −0.248924 0.620130i
\(268\) −7.24848 + 12.5547i −0.442771 + 0.766902i
\(269\) −10.2041 + 17.6740i −0.622154 + 1.07760i 0.366929 + 0.930249i \(0.380409\pi\)
−0.989084 + 0.147354i \(0.952924\pi\)
\(270\) 4.22434 3.02571i 0.257085 0.184139i
\(271\) 4.77395i 0.289997i −0.989432 0.144998i \(-0.953682\pi\)
0.989432 0.144998i \(-0.0463177\pi\)
\(272\) −1.65822 2.87212i −0.100544 0.174148i
\(273\) −25.9782 + 10.4278i −1.57227 + 0.631119i
\(274\) −3.57749 2.06547i −0.216124 0.124779i
\(275\) −6.37045 −0.384152
\(276\) −3.15791 7.86713i −0.190084 0.473545i
\(277\) 5.06954i 0.304599i 0.988334 + 0.152300i \(0.0486679\pi\)
−0.988334 + 0.152300i \(0.951332\pi\)
\(278\) −20.7544 −1.24477
\(279\) −16.6398 1.45449i −0.996201 0.0870783i
\(280\) −4.71285 −0.281647
\(281\) 22.2236i 1.32575i −0.748730 0.662875i \(-0.769336\pi\)
0.748730 0.662875i \(-0.230664\pi\)
\(282\) −2.26220 5.63571i −0.134712 0.335601i
\(283\) 2.14992 0.127800 0.0638998 0.997956i \(-0.479646\pi\)
0.0638998 + 0.997956i \(0.479646\pi\)
\(284\) −1.61036 0.929740i −0.0955571 0.0551699i
\(285\) 8.23384 3.30511i 0.487731 0.195778i
\(286\) 10.9231 + 18.9193i 0.645894 + 1.11872i
\(287\) 45.3662i 2.67788i
\(288\) −2.07422 2.16740i −0.122225 0.127715i
\(289\) 3.00061 5.19721i 0.176507 0.305718i
\(290\) 2.78554 4.82470i 0.163573 0.283316i
\(291\) 0.302713 + 0.754134i 0.0177454 + 0.0442081i
\(292\) −9.05398 5.22732i −0.529844 0.305906i
\(293\) 10.4783 6.04966i 0.612150 0.353425i −0.161656 0.986847i \(-0.551684\pi\)
0.773806 + 0.633422i \(0.218350\pi\)
\(294\) 3.72551 26.0814i 0.217276 1.52110i
\(295\) 5.62423 0.327455
\(296\) 2.46429 + 4.26827i 0.143234 + 0.248088i
\(297\) 26.9110 19.2751i 1.56153 1.11846i
\(298\) 0.0317462 + 0.0549861i 0.00183901 + 0.00318526i
\(299\) −14.5355 8.39208i −0.840611 0.485327i
\(300\) 1.06943 1.36247i 0.0617437 0.0786620i
\(301\) 24.8320 + 14.3367i 1.43129 + 0.826356i
\(302\) 2.80211 0.161244
\(303\) −25.5475 + 10.2549i −1.46767 + 0.589130i
\(304\) −2.56125 4.43621i −0.146898 0.254434i
\(305\) 0.659441 1.14219i 0.0377595 0.0654014i
\(306\) −2.78551 + 9.55144i −0.159237 + 0.546019i
\(307\) 5.45338 + 9.44553i 0.311241 + 0.539085i 0.978631 0.205623i \(-0.0659221\pi\)
−0.667391 + 0.744708i \(0.732589\pi\)
\(308\) −30.0230 −1.71072
\(309\) −26.0113 3.71549i −1.47973 0.211367i
\(310\) −5.46054 + 1.08744i −0.310138 + 0.0617627i
\(311\) 26.9183i 1.52640i −0.646164 0.763199i \(-0.723628\pi\)
0.646164 0.763199i \(-0.276372\pi\)
\(312\) −5.88003 0.839911i −0.332891 0.0475506i
\(313\) 9.74557 5.62661i 0.550852 0.318035i −0.198614 0.980078i \(-0.563644\pi\)
0.749466 + 0.662043i \(0.230311\pi\)
\(314\) 0.873360i 0.0492866i
\(315\) 9.77549 + 10.2146i 0.550787 + 0.575529i
\(316\) −0.954760 + 0.551231i −0.0537095 + 0.0310092i
\(317\) 16.9180 9.76764i 0.950212 0.548605i 0.0570654 0.998370i \(-0.481826\pi\)
0.893147 + 0.449765i \(0.148492\pi\)
\(318\) 0.316248 2.21398i 0.0177343 0.124154i
\(319\) 17.7451 30.7355i 0.993537 1.72086i
\(320\) −0.866025 0.500000i −0.0484123 0.0279508i
\(321\) 19.8300 + 15.5650i 1.10680 + 0.868756i
\(322\) 19.9761 11.5332i 1.11322 0.642719i
\(323\) −8.49422 + 14.7124i −0.472631 + 0.818621i
\(324\) −0.395219 + 8.99132i −0.0219566 + 0.499518i
\(325\) 3.42929i 0.190223i
\(326\) 2.46179i 0.136346i
\(327\) −8.49936 21.1740i −0.470016 1.17093i
\(328\) −4.81303 + 8.33642i −0.265755 + 0.460302i
\(329\) 14.3101 8.26192i 0.788940 0.455495i
\(330\) 6.81276 8.67952i 0.375030 0.477792i
\(331\) −11.4095 6.58730i −0.627125 0.362071i 0.152513 0.988301i \(-0.451263\pi\)
−0.779638 + 0.626231i \(0.784597\pi\)
\(332\) 3.19991 5.54241i 0.175618 0.304179i
\(333\) 4.13956 14.1944i 0.226846 0.777849i
\(334\) −11.3978 + 6.58051i −0.623659 + 0.360070i
\(335\) 12.5547 7.24848i 0.685938 0.396027i
\(336\) 5.04008 6.42110i 0.274959 0.350300i
\(337\) 23.5530i 1.28301i −0.767118 0.641506i \(-0.778310\pi\)
0.767118 0.641506i \(-0.221690\pi\)
\(338\) 1.07383 0.619974i 0.0584085 0.0337221i
\(339\) −0.883070 + 6.18218i −0.0479618 + 0.335770i
\(340\) 3.31644i 0.179859i
\(341\) −34.7861 + 6.92751i −1.88377 + 0.375146i
\(342\) −4.30244 + 14.7529i −0.232649 + 0.797746i
\(343\) 38.6971 2.08945
\(344\) 3.04205 + 5.26899i 0.164017 + 0.284085i
\(345\) −1.19874 + 8.39208i −0.0645378 + 0.451815i
\(346\) 1.37051 2.37379i 0.0736790 0.127616i
\(347\) 5.57362 + 9.65380i 0.299208 + 0.518243i 0.975955 0.217972i \(-0.0699443\pi\)
−0.676747 + 0.736216i \(0.736611\pi\)
\(348\) 3.59454 + 8.95489i 0.192688 + 0.480032i
\(349\) 22.1999 1.18833 0.594165 0.804343i \(-0.297482\pi\)
0.594165 + 0.804343i \(0.297482\pi\)
\(350\) 4.08145 + 2.35643i 0.218163 + 0.125956i
\(351\) 10.3761 + 14.4865i 0.553833 + 0.773233i
\(352\) −5.51697 3.18522i −0.294055 0.169773i
\(353\) −0.971322 1.68238i −0.0516983 0.0895440i 0.839018 0.544103i \(-0.183130\pi\)
−0.890716 + 0.454559i \(0.849797\pi\)
\(354\) −6.01473 + 7.66282i −0.319679 + 0.407274i
\(355\) 0.929740 + 1.61036i 0.0493455 + 0.0854688i
\(356\) 6.30402 0.334112
\(357\) −26.7997 3.82811i −1.41839 0.202605i
\(358\) −2.64335 + 1.52614i −0.139705 + 0.0806590i
\(359\) 5.87430 + 3.39153i 0.310034 + 0.178998i 0.646942 0.762540i \(-0.276048\pi\)
−0.336908 + 0.941538i \(0.609381\pi\)
\(360\) 0.712629 + 2.91413i 0.0375588 + 0.153588i
\(361\) −3.61997 + 6.26997i −0.190525 + 0.329999i
\(362\) 8.05934 13.9592i 0.423590 0.733679i
\(363\) 31.6366 40.3053i 1.66049 2.11548i
\(364\) 16.1618i 0.847106i
\(365\) 5.22732 + 9.05398i 0.273610 + 0.473907i
\(366\) 0.850962 + 2.11996i 0.0444805 + 0.110812i
\(367\) 0.773089 + 0.446343i 0.0403549 + 0.0232989i 0.520042 0.854141i \(-0.325916\pi\)
−0.479687 + 0.877440i \(0.659250\pi\)
\(368\) 4.89435 0.255136
\(369\) 28.0516 6.85982i 1.46031 0.357108i
\(370\) 4.92857i 0.256224i
\(371\) 6.08531 0.315933
\(372\) 4.35807 8.60275i 0.225955 0.446032i
\(373\) 25.6902 1.33019 0.665093 0.746761i \(-0.268392\pi\)
0.665093 + 0.746761i \(0.268392\pi\)
\(374\) 21.1272i 1.09246i
\(375\) −1.60739 + 0.645214i −0.0830052 + 0.0333187i
\(376\) 3.50612 0.180815
\(377\) 16.5453 + 9.55243i 0.852126 + 0.491975i
\(378\) −24.3713 + 2.39494i −1.25352 + 0.123182i
\(379\) 14.5013 + 25.1170i 0.744882 + 1.29017i 0.950250 + 0.311489i \(0.100828\pi\)
−0.205367 + 0.978685i \(0.565839\pi\)
\(380\) 5.12249i 0.262778i
\(381\) 4.45352 + 3.49567i 0.228161 + 0.179089i
\(382\) −4.37340 + 7.57495i −0.223763 + 0.387568i
\(383\) −1.37993 + 2.39011i −0.0705113 + 0.122129i −0.899125 0.437691i \(-0.855796\pi\)
0.828614 + 0.559820i \(0.189130\pi\)
\(384\) 1.60739 0.645214i 0.0820267 0.0329260i
\(385\) 26.0007 + 15.0115i 1.32512 + 0.765056i
\(386\) 18.6381 10.7607i 0.948656 0.547707i
\(387\) 5.11011 17.5224i 0.259761 0.890713i
\(388\) −0.469167 −0.0238183
\(389\) 0.673046 + 1.16575i 0.0341248 + 0.0591059i 0.882583 0.470156i \(-0.155802\pi\)
−0.848459 + 0.529262i \(0.822469\pi\)
\(390\) 4.67230 + 3.66740i 0.236591 + 0.185706i
\(391\) −8.11591 14.0572i −0.410439 0.710902i
\(392\) 13.1731 + 7.60549i 0.665342 + 0.384135i
\(393\) −12.7635 10.0184i −0.643832 0.505359i
\(394\) −12.2770 7.08814i −0.618507 0.357095i
\(395\) 1.10246 0.0554709
\(396\) 4.53977 + 18.5643i 0.228132 + 0.932892i
\(397\) −1.52687 2.64462i −0.0766314 0.132730i 0.825163 0.564894i \(-0.191083\pi\)
−0.901795 + 0.432165i \(0.857750\pi\)
\(398\) 3.87401 6.70999i 0.194187 0.336341i
\(399\) −41.3942 5.91281i −2.07230 0.296011i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 22.4218 1.11969 0.559845 0.828597i \(-0.310861\pi\)
0.559845 + 0.828597i \(0.310861\pi\)
\(402\) −3.55063 + 24.8571i −0.177089 + 1.23976i
\(403\) −3.72917 18.7258i −0.185763 0.932798i
\(404\) 15.8938i 0.790747i
\(405\) 4.83793 7.58910i 0.240399 0.377105i
\(406\) −22.7381 + 13.1278i −1.12847 + 0.651524i
\(407\) 31.3972i 1.55630i
\(408\) −4.51854 3.54671i −0.223701 0.175588i
\(409\) −21.5021 + 12.4143i −1.06321 + 0.613846i −0.926319 0.376740i \(-0.877045\pi\)
−0.136893 + 0.990586i \(0.543712\pi\)
\(410\) 8.33642 4.81303i 0.411706 0.237699i
\(411\) −7.08309 1.01176i −0.349383 0.0499063i
\(412\) 7.58503 13.1377i 0.373688 0.647246i
\(413\) −22.9550 13.2531i −1.12954 0.652141i
\(414\) −10.1520 10.6080i −0.498942 0.521355i
\(415\) −5.54241 + 3.19991i −0.272066 + 0.157077i
\(416\) 1.71465 2.96986i 0.0840675 0.145609i
\(417\) −33.3604 + 13.3911i −1.63367 + 0.655763i
\(418\) 32.6326i 1.59611i
\(419\) 13.9574i 0.681865i 0.940088 + 0.340933i \(0.110743\pi\)
−0.940088 + 0.340933i \(0.889257\pi\)
\(420\) −7.57539 + 3.04080i −0.369641 + 0.148376i
\(421\) −13.1223 + 22.7286i −0.639544 + 1.10772i 0.345989 + 0.938239i \(0.387544\pi\)
−0.985533 + 0.169484i \(0.945790\pi\)
\(422\) 13.3164 7.68821i 0.648231 0.374256i
\(423\) −7.27248 7.59916i −0.353600 0.369484i
\(424\) 1.11823 + 0.645608i 0.0543058 + 0.0313535i
\(425\) 1.65822 2.87212i 0.0804355 0.139318i
\(426\) −3.18835 0.455428i −0.154476 0.0220656i
\(427\) −5.38295 + 3.10785i −0.260499 + 0.150399i
\(428\) −12.6046 + 7.27724i −0.609264 + 0.351759i
\(429\) 29.7646 + 23.3630i 1.43705 + 1.12797i
\(430\) 6.08411i 0.293402i
\(431\) 0.654160 0.377680i 0.0315098 0.0181922i −0.484162 0.874978i \(-0.660876\pi\)
0.515672 + 0.856786i \(0.327542\pi\)
\(432\) −4.73251 2.14553i −0.227693 0.103227i
\(433\) 5.99857i 0.288273i 0.989558 + 0.144136i \(0.0460404\pi\)
−0.989558 + 0.144136i \(0.953960\pi\)
\(434\) 24.8494 + 8.42900i 1.19281 + 0.404605i
\(435\) 1.36448 9.55243i 0.0654219 0.458004i
\(436\) 13.1729 0.630869
\(437\) −12.5356 21.7124i −0.599661 1.03864i
\(438\) −17.9260 2.56057i −0.856538 0.122349i
\(439\) 1.21561 2.10550i 0.0580180 0.100490i −0.835558 0.549403i \(-0.814855\pi\)
0.893576 + 0.448913i \(0.148189\pi\)
\(440\) 3.18522 + 5.51697i 0.151850 + 0.263011i
\(441\) −10.8398 44.3268i −0.516180 2.11080i
\(442\) −11.3730 −0.540961
\(443\) 18.0112 + 10.3987i 0.855736 + 0.494059i 0.862582 0.505917i \(-0.168846\pi\)
−0.00684619 + 0.999977i \(0.502179\pi\)
\(444\) 6.71501 + 5.27077i 0.318680 + 0.250140i
\(445\) −5.45944 3.15201i −0.258802 0.149420i
\(446\) −5.62754 9.74718i −0.266472 0.461542i
\(447\) 0.0865064 + 0.0679009i 0.00409161 + 0.00321160i
\(448\) 2.35643 + 4.08145i 0.111331 + 0.192830i
\(449\) −19.2778 −0.909775 −0.454888 0.890549i \(-0.650321\pi\)
−0.454888 + 0.890549i \(0.650321\pi\)
\(450\) 0.839911 2.88003i 0.0395938 0.135766i
\(451\) 53.1067 30.6612i 2.50070 1.44378i
\(452\) −3.12246 1.80276i −0.146868 0.0847945i
\(453\) 4.50409 1.80796i 0.211621 0.0849456i
\(454\) 11.0278 19.1006i 0.517558 0.896437i
\(455\) −8.08088 + 13.9965i −0.378837 + 0.656165i
\(456\) −6.97923 5.47816i −0.326832 0.256538i
\(457\) 9.77722i 0.457359i 0.973502 + 0.228680i \(0.0734408\pi\)
−0.973502 + 0.228680i \(0.926559\pi\)
\(458\) −3.65326 6.32764i −0.170706 0.295671i
\(459\) 1.68532 + 17.1501i 0.0786640 + 0.800499i
\(460\) −4.23863 2.44718i −0.197627 0.114100i
\(461\) −15.6965 −0.731059 −0.365530 0.930800i \(-0.619112\pi\)
−0.365530 + 0.930800i \(0.619112\pi\)
\(462\) −48.2586 + 19.3713i −2.24519 + 0.901232i
\(463\) 37.5167i 1.74355i −0.489908 0.871774i \(-0.662970\pi\)
0.489908 0.871774i \(-0.337030\pi\)
\(464\) −5.57108 −0.258631
\(465\) −8.07557 + 5.27116i −0.374496 + 0.244444i
\(466\) −9.29519 −0.430591
\(467\) 18.6592i 0.863446i −0.902006 0.431723i \(-0.857906\pi\)
0.902006 0.431723i \(-0.142094\pi\)
\(468\) −9.99341 + 2.44381i −0.461946 + 0.112965i
\(469\) −68.3220 −3.15482
\(470\) −3.03639 1.75306i −0.140058 0.0808627i
\(471\) 0.563504 + 1.40383i 0.0259649 + 0.0646850i
\(472\) −2.81211 4.87072i −0.129438 0.224193i
\(473\) 38.7585i 1.78212i
\(474\) −1.17901 + 1.50207i −0.0541537 + 0.0689922i
\(475\) 2.56125 4.43621i 0.117518 0.203547i
\(476\) 7.81495 13.5359i 0.358198 0.620416i
\(477\) −0.920158 3.76277i −0.0421311 0.172285i
\(478\) 20.8498 + 12.0377i 0.953649 + 0.550589i
\(479\) −0.407841 + 0.235467i −0.0186347 + 0.0107588i −0.509288 0.860596i \(-0.670091\pi\)
0.490654 + 0.871355i \(0.336758\pi\)
\(480\) −1.71465 0.244922i −0.0782626 0.0111791i
\(481\) 16.9015 0.770643
\(482\) −5.72490 9.91581i −0.260762 0.451653i
\(483\) 24.6679 31.4271i 1.12243 1.42998i
\(484\) 14.7913 + 25.6193i 0.672332 + 1.16451i
\(485\) 0.406311 + 0.234584i 0.0184496 + 0.0106519i
\(486\) 5.16606 + 14.7075i 0.234337 + 0.667148i
\(487\) 16.0925 + 9.29103i 0.729222 + 0.421017i 0.818138 0.575023i \(-0.195007\pi\)
−0.0889154 + 0.996039i \(0.528340\pi\)
\(488\) −1.31888 −0.0597030
\(489\) 1.58838 + 3.95706i 0.0718292 + 0.178944i
\(490\) −7.60549 13.1731i −0.343581 0.595100i
\(491\) 1.07403 1.86028i 0.0484704 0.0839532i −0.840772 0.541389i \(-0.817899\pi\)
0.889243 + 0.457436i \(0.151232\pi\)
\(492\) −2.35764 + 16.5053i −0.106291 + 0.744117i
\(493\) 9.23808 + 16.0008i 0.416062 + 0.720641i
\(494\) −17.5665 −0.790356
\(495\) 5.35061 18.3471i 0.240492 0.824639i
\(496\) 3.67202 + 4.18524i 0.164879 + 0.187923i
\(497\) 8.76345i 0.393095i
\(498\) 1.56746 10.9734i 0.0702395 0.491731i
\(499\) 13.7161 7.91901i 0.614019 0.354504i −0.160518 0.987033i \(-0.551316\pi\)
0.774537 + 0.632529i \(0.217983\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −14.0748 + 17.9315i −0.628817 + 0.801118i
\(502\) −19.4132 + 11.2082i −0.866455 + 0.500248i
\(503\) 17.9459 10.3610i 0.800166 0.461976i −0.0433631 0.999059i \(-0.513807\pi\)
0.843529 + 0.537083i \(0.180474\pi\)
\(504\) 3.95837 13.5731i 0.176320 0.604596i
\(505\) −7.94691 + 13.7644i −0.353633 + 0.612510i
\(506\) −27.0020 15.5896i −1.20038 0.693042i
\(507\) 1.32604 1.68939i 0.0588915 0.0750283i
\(508\) −2.83079 + 1.63436i −0.125596 + 0.0725129i
\(509\) 0.867034 1.50175i 0.0384306 0.0665638i −0.846170 0.532913i \(-0.821097\pi\)
0.884601 + 0.466349i \(0.154431\pi\)
\(510\) 2.13981 + 5.33081i 0.0947526 + 0.236052i
\(511\) 49.2712i 2.17963i
\(512\) 1.00000i 0.0441942i
\(513\) 2.60310 + 26.4897i 0.114930 + 1.16955i
\(514\) 15.8934 27.5281i 0.701027 1.21421i
\(515\) −13.1377 + 7.58503i −0.578915 + 0.334236i
\(516\) 8.28939 + 6.50654i 0.364920 + 0.286434i
\(517\) −19.3432 11.1678i −0.850712 0.491159i
\(518\) −11.6138 + 20.1157i −0.510282 + 0.883834i
\(519\) 0.671337 4.69988i 0.0294684 0.206302i
\(520\) −2.96986 + 1.71465i −0.130237 + 0.0751922i
\(521\) −32.8261 + 18.9521i −1.43814 + 0.830308i −0.997720 0.0674858i \(-0.978502\pi\)
−0.440416 + 0.897794i \(0.645169\pi\)
\(522\) 11.5556 + 12.0747i 0.505777 + 0.528497i
\(523\) 8.57223i 0.374837i −0.982280 0.187419i \(-0.939988\pi\)
0.982280 0.187419i \(-0.0600121\pi\)
\(524\) 8.11286 4.68396i 0.354412 0.204620i
\(525\) 8.08088 + 1.15428i 0.352678 + 0.0503770i
\(526\) 8.90216i 0.388153i
\(527\) 5.93150 17.4865i 0.258380 0.761726i
\(528\) −10.9231 1.56027i −0.475365 0.0679018i
\(529\) 0.954681 0.0415079
\(530\) −0.645608 1.11823i −0.0280434 0.0485726i
\(531\) −4.72385 + 16.1979i −0.204998 + 0.702930i
\(532\) 12.0708 20.9072i 0.523335 0.906442i
\(533\) 16.5053 + 28.5880i 0.714924 + 1.23828i
\(534\) 10.1330 4.06744i 0.438498 0.176016i
\(535\) 14.5545 0.629245
\(536\) −12.5547 7.24848i −0.542282 0.313086i
\(537\) −3.26421 + 4.15863i −0.140861 + 0.179458i
\(538\) −17.6740 10.2041i −0.761980 0.439930i
\(539\) −48.4504 83.9185i −2.08690 3.61463i
\(540\) 3.02571 + 4.22434i 0.130206 + 0.181787i
\(541\) 17.5603 + 30.4153i 0.754974 + 1.30765i 0.945387 + 0.325950i \(0.105684\pi\)
−0.190413 + 0.981704i \(0.560983\pi\)
\(542\) 4.77395 0.205059
\(543\) 3.94783 27.6378i 0.169417 1.18605i
\(544\) 2.87212 1.65822i 0.123141 0.0710956i
\(545\) −11.4081 6.58646i −0.488669 0.282133i
\(546\) −10.4278 25.9782i −0.446268 1.11177i
\(547\) −19.3350 + 33.4893i −0.826706 + 1.43190i 0.0739019 + 0.997266i \(0.476455\pi\)
−0.900608 + 0.434632i \(0.856878\pi\)
\(548\) 2.06547 3.57749i 0.0882323 0.152823i
\(549\) 2.73565 + 2.85854i 0.116755 + 0.122000i
\(550\) 6.37045i 0.271637i
\(551\) 14.2689 + 24.7145i 0.607876 + 1.05287i
\(552\) 7.86713 3.15791i 0.334847 0.134409i
\(553\) −4.49964 2.59787i −0.191344 0.110473i
\(554\) −5.06954 −0.215384
\(555\) −3.17998 7.92213i −0.134983 0.336276i
\(556\) 20.7544i 0.880184i
\(557\) 25.0087 1.05965 0.529826 0.848107i \(-0.322257\pi\)
0.529826 + 0.848107i \(0.322257\pi\)
\(558\) 1.45449 16.6398i 0.0615737 0.704421i
\(559\) 20.8642 0.882461
\(560\) 4.71285i 0.199154i
\(561\) 13.6316 + 33.9596i 0.575526 + 1.43378i
\(562\) 22.2236 0.937447
\(563\) −27.9134 16.1158i −1.17641 0.679200i −0.221228 0.975222i \(-0.571006\pi\)
−0.955181 + 0.296022i \(0.904340\pi\)
\(564\) 5.63571 2.26220i 0.237306 0.0952559i
\(565\) 1.80276 + 3.12246i 0.0758425 + 0.131363i
\(566\) 2.14992i 0.0903679i
\(567\) −37.6289 + 19.5743i −1.58027 + 0.822044i
\(568\) 0.929740 1.61036i 0.0390110 0.0675691i
\(569\) 8.43031 14.6017i 0.353417 0.612136i −0.633429 0.773801i \(-0.718353\pi\)
0.986846 + 0.161665i \(0.0516863\pi\)
\(570\) 3.30511 + 8.23384i 0.138436 + 0.344878i
\(571\) 11.3902 + 6.57613i 0.476665 + 0.275203i 0.719026 0.694984i \(-0.244588\pi\)
−0.242361 + 0.970186i \(0.577922\pi\)
\(572\) −18.9193 + 10.9231i −0.791056 + 0.456716i
\(573\) −2.14229 + 14.9977i −0.0894953 + 0.626537i
\(574\) −45.3662 −1.89355
\(575\) 2.44718 + 4.23863i 0.102054 + 0.176763i
\(576\) 2.16740 2.07422i 0.0903082 0.0864258i
\(577\) 7.01445 + 12.1494i 0.292015 + 0.505785i 0.974286 0.225314i \(-0.0723409\pi\)
−0.682271 + 0.731099i \(0.739008\pi\)
\(578\) 5.19721 + 3.00061i 0.216175 + 0.124809i
\(579\) 23.0157 29.3223i 0.956502 1.21859i
\(580\) 4.82470 + 2.78554i 0.200335 + 0.115663i
\(581\) 30.1614 1.25131
\(582\) −0.754134 + 0.302713i −0.0312599 + 0.0125479i
\(583\) −4.11281 7.12360i −0.170335 0.295029i
\(584\) 5.22732 9.05398i 0.216308 0.374656i
\(585\) 9.87645 + 2.88030i 0.408341 + 0.119086i
\(586\) 6.04966 + 10.4783i 0.249909 + 0.432855i
\(587\) 2.63583 0.108792 0.0543961 0.998519i \(-0.482677\pi\)
0.0543961 + 0.998519i \(0.482677\pi\)
\(588\) 26.0814 + 3.72551i 1.07558 + 0.153637i
\(589\) 9.16165 27.0093i 0.377499 1.11290i
\(590\) 5.62423i 0.231546i
\(591\) −24.3073 3.47209i −0.999869 0.142823i
\(592\) −4.26827 + 2.46429i −0.175425 + 0.101282i
\(593\) 0.710550i 0.0291788i 0.999894 + 0.0145894i \(0.00464411\pi\)
−0.999894 + 0.0145894i \(0.995356\pi\)
\(594\) 19.2751 + 26.9110i 0.790868 + 1.10417i
\(595\) −13.5359 + 7.81495i −0.554917 + 0.320382i
\(596\) −0.0549861 + 0.0317462i −0.00225232 + 0.00130038i
\(597\) 1.89766 13.2851i 0.0776663 0.543724i
\(598\) 8.39208 14.5355i 0.343178 0.594401i
\(599\) −3.56655 2.05915i −0.145725 0.0841346i 0.425364 0.905022i \(-0.360146\pi\)
−0.571090 + 0.820888i \(0.693479\pi\)
\(600\) 1.36247 + 1.06943i 0.0556225 + 0.0436594i
\(601\) −32.9052 + 18.9978i −1.34223 + 0.774938i −0.987135 0.159891i \(-0.948886\pi\)
−0.355098 + 0.934829i \(0.615552\pi\)
\(602\) −14.3367 + 24.8320i −0.584322 + 1.01208i
\(603\) 10.3309 + 42.2460i 0.420709 + 1.72039i
\(604\) 2.80211i 0.114016i
\(605\) 29.5826i 1.20270i
\(606\) −10.2549 25.5475i −0.416578 1.03780i
\(607\) 4.63844 8.03401i 0.188268 0.326090i −0.756405 0.654104i \(-0.773046\pi\)
0.944673 + 0.328014i \(0.106379\pi\)
\(608\) 4.43621 2.56125i 0.179912 0.103872i
\(609\) −28.0787 + 35.7725i −1.13780 + 1.44957i
\(610\) 1.14219 + 0.659441i 0.0462458 + 0.0267000i
\(611\) 6.01176 10.4127i 0.243210 0.421252i
\(612\) −9.55144 2.78551i −0.386094 0.112598i
\(613\) 6.90442 3.98627i 0.278867 0.161004i −0.354044 0.935229i \(-0.615194\pi\)
0.632910 + 0.774225i \(0.281860\pi\)
\(614\) −9.44553 + 5.45338i −0.381190 + 0.220080i
\(615\) 10.2944 13.1152i 0.415111 0.528856i
\(616\) 30.0230i 1.20966i
\(617\) −27.4184 + 15.8300i −1.10382 + 0.637292i −0.937222 0.348733i \(-0.886612\pi\)
−0.166599 + 0.986025i \(0.553279\pi\)
\(618\) 3.71549 26.0113i 0.149459 1.04633i
\(619\) 41.1513i 1.65401i −0.562193 0.827006i \(-0.690042\pi\)
0.562193 0.827006i \(-0.309958\pi\)
\(620\) −1.08744 5.46054i −0.0436728 0.219300i
\(621\) −23.1626 10.5010i −0.929483 0.421390i
\(622\) 26.9183 1.07933
\(623\) 14.8550 + 25.7295i 0.595151 + 1.03083i
\(624\) 0.839911 5.88003i 0.0336233 0.235389i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 5.62661 + 9.74557i 0.224884 + 0.389511i
\(627\) 21.0550 + 52.4532i 0.840856 + 2.09478i
\(628\) −0.873360 −0.0348509
\(629\) 14.1555 + 8.17266i 0.564415 + 0.325865i
\(630\) −10.2146 + 9.77549i −0.406960 + 0.389465i
\(631\) −31.0070 17.9019i −1.23437 0.712663i −0.266431 0.963854i \(-0.585845\pi\)
−0.967938 + 0.251191i \(0.919178\pi\)
\(632\) −0.551231 0.954760i −0.0219268 0.0379783i
\(633\) 16.4441 20.9499i 0.653592 0.832682i
\(634\) 9.76764 + 16.9180i 0.387923 + 0.671902i
\(635\) 3.26872 0.129715
\(636\) 2.21398 + 0.316248i 0.0877899 + 0.0125400i
\(637\) 45.1744 26.0814i 1.78987 1.03338i
\(638\) 30.7355 + 17.7451i 1.21683 + 0.702537i
\(639\) −5.41877 + 1.32512i −0.214363 + 0.0524209i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 11.0148 19.0781i 0.435057 0.753541i −0.562243 0.826972i \(-0.690061\pi\)
0.997300 + 0.0734307i \(0.0233948\pi\)
\(642\) −15.5650 + 19.8300i −0.614303 + 0.782628i
\(643\) 0.891118i 0.0351422i −0.999846 0.0175711i \(-0.994407\pi\)
0.999846 0.0175711i \(-0.00559335\pi\)
\(644\) 11.5332 + 19.9761i 0.454471 + 0.787167i
\(645\) −3.92555 9.77953i −0.154568 0.385068i
\(646\) −14.7124 8.49422i −0.578853 0.334201i
\(647\) 2.41935 0.0951144 0.0475572 0.998869i \(-0.484856\pi\)
0.0475572 + 0.998869i \(0.484856\pi\)
\(648\) −8.99132 0.395219i −0.353212 0.0155257i
\(649\) 35.8288i 1.40641i
\(650\) 3.42929 0.134508
\(651\) 45.3811 2.48450i 1.77863 0.0973752i
\(652\) −2.46179 −0.0964112
\(653\) 41.5741i 1.62692i 0.581621 + 0.813460i \(0.302419\pi\)
−0.581621 + 0.813460i \(0.697581\pi\)
\(654\) 21.1740 8.49936i 0.827969 0.332351i
\(655\) −9.36792 −0.366035
\(656\) −8.33642 4.81303i −0.325482 0.187917i
\(657\) −30.4662 + 7.45028i −1.18860 + 0.290663i
\(658\) 8.26192 + 14.3101i 0.322083 + 0.557865i
\(659\) 28.1446i 1.09636i 0.836361 + 0.548180i \(0.184679\pi\)
−0.836361 + 0.548180i \(0.815321\pi\)
\(660\) 8.67952 + 6.81276i 0.337850 + 0.265186i
\(661\) 8.37062 14.4983i 0.325579 0.563920i −0.656050 0.754717i \(-0.727774\pi\)
0.981629 + 0.190797i \(0.0611073\pi\)
\(662\) 6.58730 11.4095i 0.256023 0.443444i
\(663\) −18.2809 + 7.33805i −0.709972 + 0.284986i
\(664\) 5.54241 + 3.19991i 0.215087 + 0.124181i
\(665\) −20.9072 + 12.0708i −0.810746 + 0.468085i
\(666\) 14.1944 + 4.13956i 0.550022 + 0.160405i
\(667\) −27.2668 −1.05578
\(668\) −6.58051 11.3978i −0.254608 0.440993i
\(669\) −15.3347 12.0365i −0.592872 0.465359i
\(670\) 7.24848 + 12.5547i 0.280033 + 0.485031i
\(671\) 7.27623 + 4.20094i 0.280896 + 0.162175i
\(672\) 6.42110 + 5.04008i 0.247699 + 0.194425i
\(673\) −24.4794 14.1332i −0.943611 0.544794i −0.0525207 0.998620i \(-0.516726\pi\)
−0.891091 + 0.453826i \(0.850059\pi\)
\(674\) 23.5530 0.907226
\(675\) −0.508171 5.17124i −0.0195595 0.199041i
\(676\) 0.619974 + 1.07383i 0.0238452 + 0.0413010i
\(677\) 16.1530 27.9779i 0.620812 1.07528i −0.368523 0.929619i \(-0.620136\pi\)
0.989335 0.145659i \(-0.0465303\pi\)
\(678\) −6.18218 0.883070i −0.237425 0.0339141i
\(679\) −1.10556 1.91488i −0.0424274 0.0734864i
\(680\) −3.31644 −0.127180
\(681\) 5.40189 37.8174i 0.207001 1.44917i
\(682\) −6.92751 34.7861i −0.265268 1.33203i
\(683\) 40.5655i 1.55219i −0.630613 0.776097i \(-0.717196\pi\)
0.630613 0.776097i \(-0.282804\pi\)
\(684\) −14.7529 4.30244i −0.564092 0.164508i
\(685\) −3.57749 + 2.06547i −0.136689 + 0.0789174i
\(686\) 38.6971i 1.47746i
\(687\) −9.95489 7.81383i −0.379803 0.298116i
\(688\) −5.26899 + 3.04205i −0.200878 + 0.115977i
\(689\) 3.83472 2.21398i 0.146091 0.0843459i
\(690\) −8.39208 1.19874i −0.319481 0.0456351i
\(691\) −6.78386 + 11.7500i −0.258070 + 0.446991i −0.965725 0.259568i \(-0.916420\pi\)
0.707655 + 0.706558i \(0.249753\pi\)
\(692\) 2.37379 + 1.37051i 0.0902380 + 0.0520989i
\(693\) −65.0717 + 62.2743i −2.47187 + 2.36560i
\(694\) −9.65380 + 5.57362i −0.366453 + 0.211572i
\(695\) −10.3772 + 17.9739i −0.393630 + 0.681787i
\(696\) −8.95489 + 3.59454i −0.339434 + 0.136251i
\(697\) 31.9243i 1.20922i
\(698\) 22.1999i 0.840277i
\(699\) −14.9410 + 5.99739i −0.565120 + 0.226842i
\(700\) −2.35643 + 4.08145i −0.0890645 + 0.154264i
\(701\) −1.09140 + 0.630120i −0.0412216 + 0.0237993i −0.520469 0.853880i \(-0.674243\pi\)
0.479248 + 0.877680i \(0.340910\pi\)
\(702\) −14.4865 + 10.3761i −0.546758 + 0.391619i
\(703\) 21.8642 + 12.6233i 0.824623 + 0.476096i
\(704\) 3.18522 5.51697i 0.120048 0.207929i
\(705\) −6.01176 0.858728i −0.226416 0.0323416i
\(706\) 1.68238 0.971322i 0.0633172 0.0365562i
\(707\) 64.8698 37.4526i 2.43968 1.40855i
\(708\) −7.66282 6.01473i −0.287986 0.226047i
\(709\) 52.1846i 1.95983i −0.199411 0.979916i \(-0.563903\pi\)
0.199411 0.979916i \(-0.436097\pi\)
\(710\) −1.61036 + 0.929740i −0.0604356 + 0.0348925i
\(711\) −0.925970 + 3.17512i −0.0347266 + 0.119076i
\(712\) 6.30402i 0.236253i
\(713\) 17.9722 + 20.4840i 0.673063 + 0.767134i
\(714\) 3.82811 26.7997i 0.143263 1.00296i
\(715\) 21.8461 0.816999
\(716\) −1.52614 2.64335i −0.0570345 0.0987867i
\(717\) 41.2806 + 5.89658i 1.54165 + 0.220212i
\(718\) −3.39153 + 5.87430i −0.126571 + 0.219227i
\(719\) 22.9349 + 39.7245i 0.855328 + 1.48147i 0.876340 + 0.481693i \(0.159978\pi\)
−0.0210118 + 0.999779i \(0.506689\pi\)
\(720\) −2.91413 + 0.712629i −0.108603 + 0.0265581i
\(721\) 71.4943 2.66259
\(722\) −6.26997 3.61997i −0.233344 0.134721i
\(723\) −15.6000 12.2448i −0.580169 0.455388i
\(724\) 13.9592 + 8.05934i 0.518789 + 0.299523i
\(725\) −2.78554 4.82470i −0.103452 0.179185i
\(726\) 40.3053 + 31.6366i 1.49587 + 1.17414i
\(727\) −20.8556 36.1230i −0.773492 1.33973i −0.935638 0.352961i \(-0.885175\pi\)
0.162145 0.986767i \(-0.448159\pi\)
\(728\) 16.1618 0.598994
\(729\) 17.7934 + 20.3075i 0.659014 + 0.752131i
\(730\) −9.05398 + 5.22732i −0.335103 + 0.193472i
\(731\) 17.4743 + 10.0888i 0.646310 + 0.373147i
\(732\) −2.11996 + 0.850962i −0.0783559 + 0.0314525i
\(733\) 11.9558 20.7081i 0.441598 0.764870i −0.556211 0.831041i \(-0.687745\pi\)
0.997808 + 0.0661718i \(0.0210785\pi\)
\(734\) −0.446343 + 0.773089i −0.0164748 + 0.0285352i
\(735\) −20.7244 16.2671i −0.764433 0.600021i
\(736\) 4.89435i 0.180408i
\(737\) 46.1760 + 79.9792i 1.70092 + 2.94607i
\(738\) 6.85982 + 28.0516i 0.252513 + 1.03259i
\(739\) 21.4217 + 12.3678i 0.788009 + 0.454957i 0.839261 0.543729i \(-0.182988\pi\)
−0.0512524 + 0.998686i \(0.516321\pi\)
\(740\) 4.92857 0.181178
\(741\) −28.2362 + 11.3342i −1.03728 + 0.416371i
\(742\) 6.08531i 0.223399i
\(743\) 22.6992 0.832752 0.416376 0.909193i \(-0.363300\pi\)
0.416376 + 0.909193i \(0.363300\pi\)
\(744\) 8.60275 + 4.35807i 0.315392 + 0.159775i
\(745\) 0.0634925 0.00232618
\(746\) 25.6902i 0.940583i
\(747\) −4.56070 18.6499i −0.166867 0.682365i
\(748\) −21.1272 −0.772487
\(749\) −59.4034 34.2966i −2.17055 1.25317i
\(750\) −0.645214 1.60739i −0.0235599 0.0586935i
\(751\) −2.09359 3.62621i −0.0763963 0.132322i 0.825296 0.564700i \(-0.191008\pi\)
−0.901693 + 0.432378i \(0.857675\pi\)
\(752\) 3.50612i 0.127855i
\(753\) −23.9729 + 30.5417i −0.873621 + 1.11300i
\(754\) −9.55243 + 16.5453i −0.347879 + 0.602544i
\(755\) 1.40106 2.42670i 0.0509897 0.0883168i
\(756\) −2.39494 24.3713i −0.0871030 0.886376i
\(757\) −8.87601 5.12457i −0.322604 0.186256i 0.329949 0.943999i \(-0.392969\pi\)
−0.652553 + 0.757743i \(0.726302\pi\)
\(758\) −25.1170 + 14.5013i −0.912291 + 0.526711i
\(759\) −53.4613 7.63649i −1.94052 0.277187i
\(760\) −5.12249 −0.185812
\(761\) 3.16769 + 5.48660i 0.114829 + 0.198889i 0.917711 0.397248i \(-0.130035\pi\)
−0.802883 + 0.596137i \(0.796701\pi\)
\(762\) −3.49567 + 4.45352i −0.126635 + 0.161334i
\(763\) 31.0410 + 53.7646i 1.12376 + 1.94641i
\(764\) −7.57495 4.37340i −0.274052 0.158224i
\(765\) 6.87903 + 7.18804i 0.248712 + 0.259884i
\(766\) −2.39011 1.37993i −0.0863583 0.0498590i
\(767\) −19.2871 −0.696418
\(768\) 0.645214 + 1.60739i 0.0232822 + 0.0580016i
\(769\) −2.87363 4.97727i −0.103626 0.179485i 0.809550 0.587051i \(-0.199711\pi\)
−0.913176 + 0.407566i \(0.866378\pi\)
\(770\) −15.0115 + 26.0007i −0.540976 + 0.936999i
\(771\) 7.78529 54.5030i 0.280380 1.96288i
\(772\) 10.7607 + 18.6381i 0.387287 + 0.670801i
\(773\) 23.5066 0.845474 0.422737 0.906252i \(-0.361069\pi\)
0.422737 + 0.906252i \(0.361069\pi\)
\(774\) 17.5224 + 5.11011i 0.629829 + 0.183679i
\(775\) −1.78851 + 5.27269i −0.0642453 + 0.189400i
\(776\) 0.469167i 0.0168421i
\(777\) −5.68897 + 39.8272i −0.204091 + 1.42879i
\(778\) −1.16575 + 0.673046i −0.0417942 + 0.0241299i
\(779\) 49.3095i 1.76670i
\(780\) −3.66740 + 4.67230i −0.131314 + 0.167295i
\(781\) −10.2587 + 5.92286i −0.367085 + 0.211936i
\(782\) 14.0572 8.11591i 0.502684 0.290224i
\(783\) 26.3652 + 11.9529i 0.942216 + 0.427163i
\(784\) −7.60549 + 13.1731i −0.271625 + 0.470468i
\(785\) 0.756352 + 0.436680i 0.0269954 + 0.0155858i
\(786\) 10.0184 12.7635i 0.357343 0.455258i
\(787\) 24.2990 14.0290i 0.866164 0.500080i 9.26051e−5 1.00000i \(-0.499971\pi\)
0.866072 + 0.499920i \(0.166637\pi\)
\(788\) 7.08814 12.2770i 0.252504 0.437350i
\(789\) −5.74380 14.3092i −0.204485 0.509422i
\(790\) 1.10246i 0.0392238i
\(791\) 16.9922i 0.604175i
\(792\) −18.5643 + 4.53977i −0.659654 + 0.161314i
\(793\) −2.26142 + 3.91689i −0.0803053 + 0.139093i
\(794\) 2.64462 1.52687i 0.0938539 0.0541866i
\(795\) −1.75924 1.38087i −0.0623937 0.0489743i
\(796\) 6.70999 + 3.87401i 0.237829 + 0.137311i
\(797\) −11.7819 + 20.4069i −0.417338 + 0.722850i −0.995671 0.0929505i \(-0.970370\pi\)
0.578333 + 0.815801i \(0.303704\pi\)
\(798\) 5.91281 41.3942i 0.209311 1.46534i
\(799\) 10.0700 5.81393i 0.356252 0.205682i
\(800\) −0.866025 + 0.500000i −0.0306186 + 0.0176777i
\(801\) 13.6633 13.0759i 0.482770 0.462015i
\(802\) 22.4218i 0.791740i
\(803\) −57.6779 + 33.3004i −2.03541 + 1.17514i
\(804\) −24.8571 3.55063i −0.876644 0.125221i
\(805\) 23.0664i 0.812982i
\(806\) 18.7258 3.72917i 0.659588 0.131354i
\(807\) −34.9928 4.99842i −1.23181 0.175953i
\(808\) 15.8938 0.559142
\(809\) −2.84021 4.91939i −0.0998566 0.172957i 0.811769 0.583979i \(-0.198505\pi\)
−0.911625 + 0.411023i \(0.865172\pi\)
\(810\) 7.58910 + 4.83793i 0.266654 + 0.169988i
\(811\) −5.10925 + 8.84947i −0.179410 + 0.310747i −0.941679 0.336514i \(-0.890752\pi\)
0.762269 + 0.647261i \(0.224085\pi\)
\(812\) −13.1278 22.7381i −0.460697 0.797950i
\(813\) 7.67359 3.08022i 0.269124 0.108028i
\(814\) 31.3972 1.10047
\(815\) 2.13197 + 1.23090i 0.0746798 + 0.0431164i
\(816\) 3.54671 4.51854i 0.124160 0.158180i
\(817\) 26.9904 + 15.5829i 0.944274 + 0.545177i
\(818\) −12.4143 21.5021i −0.434055 0.751805i
\(819\) −33.5230 35.0289i −1.17139 1.22401i
\(820\) 4.81303 + 8.33642i 0.168078 + 0.291120i
\(821\) −27.0881 −0.945381 −0.472691 0.881228i \(-0.656717\pi\)
−0.472691 + 0.881228i \(0.656717\pi\)
\(822\) 1.01176 7.08309i 0.0352891 0.247051i
\(823\) −17.4328 + 10.0649i −0.607671 + 0.350839i −0.772053 0.635558i \(-0.780770\pi\)
0.164383 + 0.986397i \(0.447437\pi\)
\(824\) 13.1377 + 7.58503i 0.457672 + 0.264237i
\(825\) −4.11030 10.2398i −0.143102 0.356504i
\(826\) 13.2531 22.9550i 0.461134 0.798707i
\(827\) −15.6535 + 27.1126i −0.544324 + 0.942798i 0.454325 + 0.890836i \(0.349881\pi\)
−0.998649 + 0.0519614i \(0.983453\pi\)
\(828\) 10.6080 10.1520i 0.368654 0.352805i
\(829\) 44.6947i 1.55231i −0.630541 0.776156i \(-0.717167\pi\)
0.630541 0.776156i \(-0.282833\pi\)
\(830\) −3.19991 5.54241i −0.111070 0.192380i
\(831\) −8.14873 + 3.27094i −0.282676 + 0.113468i
\(832\) 2.96986 + 1.71465i 0.102961 + 0.0594447i
\(833\) 50.4463 1.74786
\(834\) −13.3911 33.3604i −0.463694 1.15518i
\(835\) 13.1610i 0.455456i
\(836\) −32.6326 −1.12862
\(837\) −8.39833 27.6852i −0.290289 0.956939i
\(838\) −13.9574 −0.482152
\(839\) 3.44221i 0.118838i 0.998233 + 0.0594191i \(0.0189248\pi\)
−0.998233 + 0.0594191i \(0.981075\pi\)
\(840\) −3.04080 7.57539i −0.104918 0.261376i
\(841\) 2.03692 0.0702388
\(842\) −22.7286 13.1223i −0.783278 0.452226i
\(843\) 35.7220 14.3390i 1.23033 0.493861i
\(844\) 7.68821 + 13.3164i 0.264639 + 0.458369i
\(845\) 1.23995i 0.0426555i
\(846\) 7.59916 7.27248i 0.261265 0.250033i
\(847\) −69.7092 + 120.740i −2.39524 + 4.14867i
\(848\) −0.645608 + 1.11823i −0.0221703 + 0.0384000i
\(849\) 1.38716 + 3.45576i 0.0476072 + 0.118601i
\(850\) 2.87212 + 1.65822i 0.0985130 + 0.0568765i
\(851\) −20.8904 + 12.0611i −0.716114 + 0.413449i
\(852\) 0.455428 3.18835i 0.0156027 0.109231i
\(853\) −37.7187 −1.29146 −0.645732 0.763564i \(-0.723448\pi\)
−0.645732 + 0.763564i \(0.723448\pi\)
\(854\) −3.10785 5.38295i −0.106348 0.184201i
\(855\) 10.6252 + 11.1025i 0.363374 + 0.379697i
\(856\) −7.27724 12.6046i −0.248731 0.430815i
\(857\) −17.6018 10.1624i −0.601265 0.347140i 0.168274 0.985740i \(-0.446181\pi\)
−0.769539 + 0.638600i \(0.779514\pi\)
\(858\) −23.3630 + 29.7646i −0.797598 + 1.01615i
\(859\) −19.1802 11.0737i −0.654420 0.377830i 0.135728 0.990746i \(-0.456663\pi\)
−0.790148 + 0.612917i \(0.789996\pi\)
\(860\) 6.08411 0.207466
\(861\) −72.9212 + 29.2709i −2.48515 + 0.997551i
\(862\) 0.377680 + 0.654160i 0.0128638 + 0.0222808i
\(863\) 9.13662 15.8251i 0.311014 0.538693i −0.667568 0.744549i \(-0.732665\pi\)
0.978582 + 0.205856i \(0.0659980\pi\)
\(864\) 2.14553 4.73251i 0.0729925 0.161003i
\(865\) −1.37051 2.37379i −0.0465987 0.0807113i
\(866\) −5.99857 −0.203840
\(867\) 10.2900 + 1.46983i 0.349466 + 0.0499182i
\(868\) −8.42900 + 24.8494i −0.286099 + 0.843443i
\(869\) 7.02318i 0.238245i
\(870\) 9.55243 + 1.36448i 0.323858 + 0.0462603i
\(871\) −43.0538 + 24.8571i −1.45882 + 0.842252i
\(872\) 13.1729i 0.446092i
\(873\) −1.01687 + 0.973156i −0.0344159 + 0.0329363i
\(874\) 21.7124 12.5356i 0.734432 0.424024i
\(875\) 4.08145 2.35643i 0.137978 0.0796617i
\(876\) 2.56057 17.9260i 0.0865138 0.605664i
\(877\) 13.5383 23.4490i 0.457155 0.791816i −0.541654 0.840601i \(-0.682202\pi\)
0.998809 + 0.0487856i \(0.0155351\pi\)
\(878\) 2.10550 + 1.21561i 0.0710573 + 0.0410250i
\(879\) 16.4849 + 12.9394i 0.556023 + 0.436435i
\(880\) −5.51697 + 3.18522i −0.185977 + 0.107374i
\(881\) −13.6476 + 23.6383i −0.459798 + 0.796394i −0.998950 0.0458146i \(-0.985412\pi\)
0.539152 + 0.842209i \(0.318745\pi\)
\(882\) 44.3268 10.8398i 1.49256 0.364995i
\(883\) 18.0675i 0.608019i −0.952669 0.304010i \(-0.901674\pi\)
0.952669 0.304010i \(-0.0983255\pi\)
\(884\) 11.3730i 0.382517i
\(885\) 3.62883 + 9.04032i 0.121982 + 0.303887i
\(886\) −10.3987 + 18.0112i −0.349353 + 0.605097i
\(887\) −3.97057 + 2.29241i −0.133319 + 0.0769716i −0.565176 0.824970i \(-0.691192\pi\)
0.431857 + 0.901942i \(0.357858\pi\)
\(888\) −5.27077 + 6.71501i −0.176876 + 0.225341i
\(889\) −13.3411 7.70249i −0.447446 0.258333i
\(890\) 3.15201 5.45944i 0.105656 0.183001i
\(891\) 48.3460 + 30.8198i 1.61965 + 1.03250i
\(892\) 9.74718 5.62754i 0.326360 0.188424i
\(893\) 15.5539 8.98005i 0.520492 0.300506i
\(894\) −0.0679009 + 0.0865064i −0.00227095 + 0.00289321i
\(895\) 3.05228i 0.102026i
\(896\) −4.08145 + 2.35643i −0.136352 + 0.0787227i
\(897\) 4.11082 28.7789i 0.137256 0.960900i
\(898\) 19.2778i 0.643308i
\(899\) −20.4571 23.3163i −0.682284 0.777643i
\(900\) 2.88003 + 0.839911i 0.0960009 + 0.0279970i
\(901\) 4.28224 0.142662
\(902\) 30.6612 + 53.1067i 1.02091 + 1.76826i
\(903\) −7.02278 + 49.1649i −0.233704 + 1.63611i
\(904\) 1.80276 3.12246i 0.0599588 0.103852i
\(905\) −8.05934 13.9592i −0.267902 0.464019i
\(906\) 1.80796 + 4.50409i 0.0600656 + 0.149638i
\(907\) −44.5709 −1.47995 −0.739977 0.672633i \(-0.765163\pi\)
−0.739977 + 0.672633i \(0.765163\pi\)
\(908\) 19.1006 + 11.0278i 0.633877 + 0.365969i
\(909\) −32.9673 34.4482i −1.09346 1.14257i
\(910\) −13.9965 8.08088i −0.463979 0.267878i
\(911\) 4.72481 + 8.18361i 0.156540 + 0.271135i 0.933619 0.358268i \(-0.116633\pi\)
−0.777079 + 0.629403i \(0.783299\pi\)
\(912\) 5.47816 6.97923i 0.181400 0.231105i
\(913\) −20.3849 35.3076i −0.674640 1.16851i
\(914\) −9.77722 −0.323402
\(915\) 2.26142 + 0.323024i 0.0747602 + 0.0106788i
\(916\) 6.32764 3.65326i 0.209071 0.120707i
\(917\) 38.2347 + 22.0748i 1.26262 + 0.728975i
\(918\) −17.1501 + 1.68532i −0.566038 + 0.0556238i
\(919\) −18.8216 + 32.6000i −0.620867 + 1.07537i 0.368457 + 0.929645i \(0.379886\pi\)
−0.989325 + 0.145729i \(0.953447\pi\)
\(920\) 2.44718 4.23863i 0.0806810 0.139744i
\(921\) −11.6640 + 14.8601i −0.384343 + 0.489657i
\(922\) 15.6965i 0.516937i
\(923\) −3.18835 5.52238i −0.104946 0.181771i
\(924\) −19.3713 48.2586i −0.637267 1.58759i
\(925\) −4.26827 2.46429i −0.140340 0.0810252i
\(926\) 37.5167 1.23287
\(927\) −10.8106 44.2076i −0.355068 1.45197i
\(928\) 5.57108i 0.182880i
\(929\) 25.0170 0.820782 0.410391 0.911910i \(-0.365392\pi\)
0.410391 + 0.911910i \(0.365392\pi\)
\(930\) −5.27116 8.07557i −0.172848 0.264808i
\(931\) 77.9181 2.55366
\(932\) 9.29519i 0.304474i
\(933\) 43.2682 17.3681i 1.41654 0.568605i
\(934\) 18.6592 0.610548
\(935\) 18.2967 + 10.5636i 0.598366 + 0.345467i
\(936\) −2.44381 9.99341i −0.0798786 0.326645i
\(937\) −14.2317 24.6500i −0.464929 0.805281i 0.534269 0.845314i \(-0.320587\pi\)
−0.999198 + 0.0400334i \(0.987254\pi\)
\(938\) 68.3220i 2.23079i
\(939\) 15.3321 + 12.0345i 0.500345 + 0.392733i
\(940\) 1.75306 3.03639i 0.0571786 0.0990362i
\(941\) −26.5777 + 46.0340i −0.866409 + 1.50067i −0.000768544 1.00000i \(0.500245\pi\)
−0.865641 + 0.500665i \(0.833089\pi\)
\(942\) −1.40383 + 0.563504i −0.0457392 + 0.0183600i
\(943\) −40.8014 23.5567i −1.32868 0.767111i
\(944\) 4.87072 2.81211i 0.158529 0.0915265i
\(945\) −10.1116 + 22.3036i −0.328930 + 0.725537i
\(946\) 38.7585 1.26015
\(947\) 24.9772 + 43.2619i 0.811651 + 1.40582i 0.911708 + 0.410840i \(0.134764\pi\)
−0.100056 + 0.994982i \(0.531902\pi\)
\(948\) −1.50207 1.17901i −0.0487849 0.0382924i
\(949\) −17.9260 31.0488i −0.581903 1.00789i
\(950\) 4.43621 + 2.56125i 0.143930 + 0.0830978i
\(951\) 26.6162 + 20.8917i 0.863088 + 0.677458i
\(952\) 13.5359 + 7.81495i 0.438701 + 0.253284i
\(953\) −9.00841 −0.291811 −0.145905 0.989299i \(-0.546610\pi\)
−0.145905 + 0.989299i \(0.546610\pi\)
\(954\) 3.76277 0.920158i 0.121824 0.0297912i
\(955\) 4.37340 + 7.57495i 0.141520 + 0.245120i
\(956\) −12.0377 + 20.8498i −0.389326 + 0.674332i
\(957\) 60.8533 + 8.69236i 1.96711 + 0.280984i
\(958\) −0.235467 0.407841i −0.00760760 0.0131768i
\(959\) 19.4685 0.628670
\(960\) 0.244922 1.71465i 0.00790484 0.0553400i
\(961\) −4.03249 + 30.7366i −0.130080 + 0.991503i
\(962\) 16.9015i 0.544927i
\(963\) −12.2245 + 41.9173i −0.393928 + 1.35077i
\(964\) 9.91581 5.72490i 0.319367 0.184386i
\(965\) 21.5215i 0.692800i
\(966\) 31.4271 + 24.6679i 1.01115 + 0.793677i
\(967\) 19.0116 10.9764i 0.611372 0.352976i −0.162130 0.986769i \(-0.551836\pi\)
0.773502 + 0.633794i \(0.218503\pi\)
\(968\) −25.6193 + 14.7913i −0.823435 + 0.475410i
\(969\) −29.1292 4.16085i −0.935764 0.133666i
\(970\) −0.234584 + 0.406311i −0.00753202 + 0.0130458i
\(971\) 2.19230 + 1.26572i 0.0703542 + 0.0406190i 0.534764 0.845001i \(-0.320400\pi\)
−0.464410 + 0.885620i \(0.653734\pi\)
\(972\) −14.7075 + 5.16606i −0.471745 + 0.165701i
\(973\) 84.7082 48.9063i 2.71562 1.56786i
\(974\) −9.29103 + 16.0925i −0.297704 + 0.515638i
\(975\) 5.51221 2.21263i 0.176532 0.0708608i
\(976\) 1.31888i 0.0422164i
\(977\) 33.8056i 1.08154i −0.841171 0.540769i \(-0.818133\pi\)
0.841171 0.540769i \(-0.181867\pi\)
\(978\) −3.95706 + 1.58838i −0.126533 + 0.0507909i
\(979\) 20.0797 34.7791i 0.641750 1.11154i
\(980\) 13.1731 7.60549i 0.420799 0.242948i
\(981\) 28.5510 27.3235i 0.911562 0.872374i
\(982\) 1.86028 + 1.07403i 0.0593639 + 0.0342738i
\(983\) −15.2194 + 26.3608i −0.485424 + 0.840779i −0.999860 0.0167499i \(-0.994668\pi\)
0.514436 + 0.857529i \(0.328001\pi\)
\(984\) −16.5053 2.35764i −0.526170 0.0751588i
\(985\) −12.2770 + 7.08814i −0.391178 + 0.225847i
\(986\) −16.0008 + 9.23808i −0.509570 + 0.294200i
\(987\) 22.5132 + 17.6711i 0.716603 + 0.562478i
\(988\) 17.5665i 0.558866i
\(989\) −25.7883 + 14.8889i −0.820020 + 0.473439i
\(990\) 18.3471 + 5.35061i 0.583108 + 0.170053i
\(991\) 24.1624i 0.767543i 0.923428 + 0.383771i \(0.125375\pi\)
−0.923428 + 0.383771i \(0.874625\pi\)
\(992\) −4.18524 + 3.67202i −0.132882 + 0.116587i
\(993\) 3.22675 22.5898i 0.102398 0.716865i
\(994\) 8.76345 0.277960
\(995\) −3.87401 6.70999i −0.122814 0.212721i
\(996\) 10.9734 + 1.56746i 0.347706 + 0.0496668i
\(997\) −31.2750 + 54.1699i −0.990490 + 1.71558i −0.376091 + 0.926583i \(0.622732\pi\)
−0.614399 + 0.788996i \(0.710601\pi\)
\(998\) 7.91901 + 13.7161i 0.250672 + 0.434177i
\(999\) 25.4868 2.50456i 0.806368 0.0792407i
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 930.2.o.d.161.15 yes 36
3.2 odd 2 inner 930.2.o.d.161.3 36
31.26 odd 6 inner 930.2.o.d.491.12 yes 36
93.26 even 6 inner 930.2.o.d.491.6 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.o.d.161.3 36 3.2 odd 2 inner
930.2.o.d.161.15 yes 36 1.1 even 1 trivial
930.2.o.d.491.6 yes 36 93.26 even 6 inner
930.2.o.d.491.12 yes 36 31.26 odd 6 inner