Properties

Label 891.2.f.e.487.4
Level $891$
Weight $2$
Character 891.487
Analytic conductor $7.115$
Analytic rank $0$
Dimension $36$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\), degree \(4\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 487.4
Character \(\chi\) \(=\) 891.487
Dual form 891.2.f.e.730.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.537447 + 0.390478i) q^{2} +(-0.481658 + 1.48239i) q^{4} +(0.903367 + 0.656335i) q^{5} +(-1.20657 + 3.71344i) q^{7} +(-0.730548 - 2.24840i) q^{8} -0.741796 q^{10} +(1.17816 + 3.10031i) q^{11} +(-2.16655 + 1.57409i) q^{13} +(-0.801549 - 2.46691i) q^{14} +(-1.25142 - 0.909207i) q^{16} +(4.48727 + 3.26019i) q^{17} +(-1.58598 - 4.88115i) q^{19} +(-1.40806 + 1.02301i) q^{20} +(-1.84380 - 1.20620i) q^{22} -2.11438 q^{23} +(-1.15979 - 3.56946i) q^{25} +(0.549758 - 1.69198i) q^{26} +(-4.92362 - 3.57722i) q^{28} +(-0.334678 + 1.03003i) q^{29} +(0.348009 - 0.252843i) q^{31} +5.75580 q^{32} -3.68470 q^{34} +(-3.52724 + 2.56269i) q^{35} +(-2.69024 + 8.27970i) q^{37} +(2.75836 + 2.00407i) q^{38} +(0.815747 - 2.51061i) q^{40} +(0.902044 + 2.77621i) q^{41} -2.23257 q^{43} +(-5.16335 + 0.253209i) q^{44} +(1.13637 - 0.825618i) q^{46} +(-3.96638 - 12.2073i) q^{47} +(-6.67071 - 4.84655i) q^{49} +(2.01712 + 1.46552i) q^{50} +(-1.28988 - 3.96985i) q^{52} +(4.56381 - 3.31581i) q^{53} +(-0.970527 + 3.57399i) q^{55} +9.23074 q^{56} +(-0.222333 - 0.684272i) q^{58} +(0.734030 - 2.25911i) q^{59} +(3.30439 + 2.40078i) q^{61} +(-0.0883065 + 0.271779i) q^{62} +(-0.590604 + 0.429099i) q^{64} -2.99032 q^{65} -9.75169 q^{67} +(-6.99421 + 5.08159i) q^{68} +(0.895028 - 2.75461i) q^{70} +(5.11062 + 3.71308i) q^{71} +(-3.60705 + 11.1014i) q^{73} +(-1.78718 - 5.50038i) q^{74} +7.99967 q^{76} +(-12.9344 + 0.634298i) q^{77} +(-3.65248 + 2.65368i) q^{79} +(-0.533744 - 1.64269i) q^{80} +(-1.56885 - 1.13983i) q^{82} +(0.389949 + 0.283315i) q^{83} +(1.91387 + 5.89030i) q^{85} +(1.19989 - 0.871768i) q^{86} +(6.11002 - 4.91390i) q^{88} -16.0830 q^{89} +(-3.23120 - 9.94461i) q^{91} +(1.01841 - 3.13433i) q^{92} +(6.89838 + 5.01197i) q^{94} +(1.77094 - 5.45040i) q^{95} +(-6.48480 + 4.71148i) q^{97} +5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.537447 + 0.390478i −0.380032 + 0.276109i −0.761359 0.648331i \(-0.775467\pi\)
0.381327 + 0.924440i \(0.375467\pi\)
\(3\) 0 0
\(4\) −0.481658 + 1.48239i −0.240829 + 0.741196i
\(5\) 0.903367 + 0.656335i 0.403998 + 0.293522i 0.771168 0.636632i \(-0.219673\pi\)
−0.367169 + 0.930154i \(0.619673\pi\)
\(6\) 0 0
\(7\) −1.20657 + 3.71344i −0.456041 + 1.40355i 0.413869 + 0.910337i \(0.364177\pi\)
−0.869909 + 0.493212i \(0.835823\pi\)
\(8\) −0.730548 2.24840i −0.258288 0.794928i
\(9\) 0 0
\(10\) −0.741796 −0.234576
\(11\) 1.17816 + 3.10031i 0.355230 + 0.934779i
\(12\) 0 0
\(13\) −2.16655 + 1.57409i −0.600893 + 0.436574i −0.846196 0.532872i \(-0.821113\pi\)
0.245303 + 0.969447i \(0.421113\pi\)
\(14\) −0.801549 2.46691i −0.214223 0.659311i
\(15\) 0 0
\(16\) −1.25142 0.909207i −0.312854 0.227302i
\(17\) 4.48727 + 3.26019i 1.08832 + 0.790713i 0.979115 0.203306i \(-0.0651688\pi\)
0.109207 + 0.994019i \(0.465169\pi\)
\(18\) 0 0
\(19\) −1.58598 4.88115i −0.363849 1.11981i −0.950699 0.310116i \(-0.899632\pi\)
0.586850 0.809696i \(-0.300368\pi\)
\(20\) −1.40806 + 1.02301i −0.314852 + 0.228753i
\(21\) 0 0
\(22\) −1.84380 1.20620i −0.393100 0.257164i
\(23\) −2.11438 −0.440878 −0.220439 0.975401i \(-0.570749\pi\)
−0.220439 + 0.975401i \(0.570749\pi\)
\(24\) 0 0
\(25\) −1.15979 3.56946i −0.231958 0.713892i
\(26\) 0.549758 1.69198i 0.107816 0.331825i
\(27\) 0 0
\(28\) −4.92362 3.57722i −0.930476 0.676030i
\(29\) −0.334678 + 1.03003i −0.0621481 + 0.191272i −0.977310 0.211814i \(-0.932063\pi\)
0.915162 + 0.403087i \(0.132063\pi\)
\(30\) 0 0
\(31\) 0.348009 0.252843i 0.0625042 0.0454120i −0.556094 0.831119i \(-0.687701\pi\)
0.618599 + 0.785707i \(0.287701\pi\)
\(32\) 5.75580 1.01749
\(33\) 0 0
\(34\) −3.68470 −0.631921
\(35\) −3.52724 + 2.56269i −0.596212 + 0.433173i
\(36\) 0 0
\(37\) −2.69024 + 8.27970i −0.442273 + 1.36118i 0.443175 + 0.896435i \(0.353852\pi\)
−0.885447 + 0.464740i \(0.846148\pi\)
\(38\) 2.75836 + 2.00407i 0.447465 + 0.325102i
\(39\) 0 0
\(40\) 0.815747 2.51061i 0.128981 0.396962i
\(41\) 0.902044 + 2.77621i 0.140876 + 0.433571i 0.996458 0.0840968i \(-0.0268005\pi\)
−0.855582 + 0.517667i \(0.826800\pi\)
\(42\) 0 0
\(43\) −2.23257 −0.340463 −0.170232 0.985404i \(-0.554452\pi\)
−0.170232 + 0.985404i \(0.554452\pi\)
\(44\) −5.16335 + 0.253209i −0.778404 + 0.0381728i
\(45\) 0 0
\(46\) 1.13637 0.825618i 0.167548 0.121731i
\(47\) −3.96638 12.2073i −0.578556 1.78061i −0.623739 0.781633i \(-0.714387\pi\)
0.0451833 0.998979i \(-0.485613\pi\)
\(48\) 0 0
\(49\) −6.67071 4.84655i −0.952958 0.692365i
\(50\) 2.01712 + 1.46552i 0.285264 + 0.207256i
\(51\) 0 0
\(52\) −1.28988 3.96985i −0.178875 0.550519i
\(53\) 4.56381 3.31581i 0.626888 0.455461i −0.228433 0.973560i \(-0.573360\pi\)
0.855321 + 0.518099i \(0.173360\pi\)
\(54\) 0 0
\(55\) −0.970527 + 3.57399i −0.130866 + 0.481917i
\(56\) 9.23074 1.23351
\(57\) 0 0
\(58\) −0.222333 0.684272i −0.0291938 0.0898493i
\(59\) 0.734030 2.25911i 0.0955625 0.294111i −0.891837 0.452356i \(-0.850584\pi\)
0.987400 + 0.158245i \(0.0505836\pi\)
\(60\) 0 0
\(61\) 3.30439 + 2.40078i 0.423084 + 0.307389i 0.778878 0.627176i \(-0.215789\pi\)
−0.355793 + 0.934565i \(0.615789\pi\)
\(62\) −0.0883065 + 0.271779i −0.0112149 + 0.0345160i
\(63\) 0 0
\(64\) −0.590604 + 0.429099i −0.0738255 + 0.0536374i
\(65\) −2.99032 −0.370904
\(66\) 0 0
\(67\) −9.75169 −1.19136 −0.595679 0.803223i \(-0.703117\pi\)
−0.595679 + 0.803223i \(0.703117\pi\)
\(68\) −6.99421 + 5.08159i −0.848172 + 0.616233i
\(69\) 0 0
\(70\) 0.895028 2.75461i 0.106976 0.329239i
\(71\) 5.11062 + 3.71308i 0.606519 + 0.440662i 0.848187 0.529697i \(-0.177694\pi\)
−0.241668 + 0.970359i \(0.577694\pi\)
\(72\) 0 0
\(73\) −3.60705 + 11.1014i −0.422174 + 1.29932i 0.483501 + 0.875344i \(0.339365\pi\)
−0.905675 + 0.423973i \(0.860635\pi\)
\(74\) −1.78718 5.50038i −0.207756 0.639406i
\(75\) 0 0
\(76\) 7.99967 0.917625
\(77\) −12.9344 + 0.634298i −1.47401 + 0.0722850i
\(78\) 0 0
\(79\) −3.65248 + 2.65368i −0.410936 + 0.298562i −0.773980 0.633209i \(-0.781737\pi\)
0.363045 + 0.931772i \(0.381737\pi\)
\(80\) −0.533744 1.64269i −0.0596744 0.183659i
\(81\) 0 0
\(82\) −1.56885 1.13983i −0.173250 0.125874i
\(83\) 0.389949 + 0.283315i 0.0428025 + 0.0310978i 0.608981 0.793185i \(-0.291579\pi\)
−0.566178 + 0.824283i \(0.691579\pi\)
\(84\) 0 0
\(85\) 1.91387 + 5.89030i 0.207589 + 0.638893i
\(86\) 1.19989 0.871768i 0.129387 0.0940052i
\(87\) 0 0
\(88\) 6.11002 4.91390i 0.651330 0.523824i
\(89\) −16.0830 −1.70480 −0.852399 0.522891i \(-0.824853\pi\)
−0.852399 + 0.522891i \(0.824853\pi\)
\(90\) 0 0
\(91\) −3.23120 9.94461i −0.338722 1.04248i
\(92\) 1.01841 3.13433i 0.106176 0.326777i
\(93\) 0 0
\(94\) 6.89838 + 5.01197i 0.711513 + 0.516945i
\(95\) 1.77094 5.45040i 0.181695 0.559199i
\(96\) 0 0
\(97\) −6.48480 + 4.71148i −0.658432 + 0.478379i −0.866133 0.499814i \(-0.833402\pi\)
0.207701 + 0.978192i \(0.433402\pi\)
\(98\) 5.47762 0.553323
\(99\) 0 0
\(100\) 5.84996 0.584996
\(101\) 1.42493 1.03527i 0.141786 0.103014i −0.514631 0.857412i \(-0.672071\pi\)
0.656417 + 0.754398i \(0.272071\pi\)
\(102\) 0 0
\(103\) 0.830534 2.55612i 0.0818350 0.251862i −0.901765 0.432227i \(-0.857728\pi\)
0.983600 + 0.180365i \(0.0577279\pi\)
\(104\) 5.12195 + 3.72131i 0.502248 + 0.364905i
\(105\) 0 0
\(106\) −1.15806 + 3.56414i −0.112481 + 0.346179i
\(107\) 3.17558 + 9.77342i 0.306995 + 0.944833i 0.978925 + 0.204219i \(0.0654653\pi\)
−0.671931 + 0.740614i \(0.734535\pi\)
\(108\) 0 0
\(109\) 2.36284 0.226319 0.113160 0.993577i \(-0.463903\pi\)
0.113160 + 0.993577i \(0.463903\pi\)
\(110\) −0.873957 2.29980i −0.0833285 0.219277i
\(111\) 0 0
\(112\) 4.88620 3.55004i 0.461703 0.335447i
\(113\) −0.473548 1.45743i −0.0445476 0.137103i 0.926309 0.376765i \(-0.122964\pi\)
−0.970857 + 0.239661i \(0.922964\pi\)
\(114\) 0 0
\(115\) −1.91006 1.38774i −0.178114 0.129407i
\(116\) −1.36571 0.992247i −0.126803 0.0921279i
\(117\) 0 0
\(118\) 0.487631 + 1.50077i 0.0448901 + 0.138157i
\(119\) −17.5207 + 12.7296i −1.60612 + 1.16692i
\(120\) 0 0
\(121\) −8.22386 + 7.30535i −0.747624 + 0.664123i
\(122\) −2.71339 −0.245658
\(123\) 0 0
\(124\) 0.207191 + 0.637669i 0.0186063 + 0.0572644i
\(125\) 3.02032 9.29560i 0.270146 0.831424i
\(126\) 0 0
\(127\) 6.19006 + 4.49734i 0.549279 + 0.399074i 0.827519 0.561437i \(-0.189751\pi\)
−0.278241 + 0.960511i \(0.589751\pi\)
\(128\) −3.40742 + 10.4869i −0.301176 + 0.926924i
\(129\) 0 0
\(130\) 1.60714 1.16765i 0.140955 0.102410i
\(131\) 5.35912 0.468229 0.234114 0.972209i \(-0.424781\pi\)
0.234114 + 0.972209i \(0.424781\pi\)
\(132\) 0 0
\(133\) 20.0394 1.73764
\(134\) 5.24101 3.80782i 0.452754 0.328945i
\(135\) 0 0
\(136\) 4.05203 12.4709i 0.347459 1.06937i
\(137\) 13.5358 + 9.83435i 1.15644 + 0.840205i 0.989324 0.145731i \(-0.0465535\pi\)
0.167119 + 0.985937i \(0.446554\pi\)
\(138\) 0 0
\(139\) 4.24593 13.0676i 0.360135 1.10838i −0.592837 0.805323i \(-0.701992\pi\)
0.952972 0.303059i \(-0.0980079\pi\)
\(140\) −2.09998 6.46308i −0.177481 0.546230i
\(141\) 0 0
\(142\) −4.19656 −0.352168
\(143\) −7.43273 4.86244i −0.621556 0.406618i
\(144\) 0 0
\(145\) −0.978384 + 0.710837i −0.0812503 + 0.0590318i
\(146\) −2.39624 7.37487i −0.198314 0.610348i
\(147\) 0 0
\(148\) −10.9780 7.97597i −0.902385 0.655621i
\(149\) 4.49786 + 3.26788i 0.368479 + 0.267716i 0.756580 0.653901i \(-0.226869\pi\)
−0.388101 + 0.921617i \(0.626869\pi\)
\(150\) 0 0
\(151\) −0.0506502 0.155885i −0.00412186 0.0126858i 0.948974 0.315353i \(-0.102123\pi\)
−0.953096 + 0.302667i \(0.902123\pi\)
\(152\) −9.81611 + 7.13182i −0.796192 + 0.578467i
\(153\) 0 0
\(154\) 6.70385 5.39148i 0.540211 0.434458i
\(155\) 0.480329 0.0385810
\(156\) 0 0
\(157\) 7.37099 + 22.6856i 0.588269 + 1.81051i 0.585727 + 0.810509i \(0.300809\pi\)
0.00254199 + 0.999997i \(0.499191\pi\)
\(158\) 0.926808 2.85242i 0.0737329 0.226926i
\(159\) 0 0
\(160\) 5.19960 + 3.77773i 0.411065 + 0.298656i
\(161\) 2.55114 7.85161i 0.201058 0.618794i
\(162\) 0 0
\(163\) 3.39466 2.46636i 0.265890 0.193180i −0.446850 0.894609i \(-0.647454\pi\)
0.712740 + 0.701429i \(0.247454\pi\)
\(164\) −4.54990 −0.355288
\(165\) 0 0
\(166\) −0.320205 −0.0248527
\(167\) 12.8151 9.31075i 0.991666 0.720488i 0.0313807 0.999508i \(-0.490010\pi\)
0.960285 + 0.279020i \(0.0900096\pi\)
\(168\) 0 0
\(169\) −1.80104 + 5.54304i −0.138542 + 0.426387i
\(170\) −3.32864 2.41840i −0.255295 0.185482i
\(171\) 0 0
\(172\) 1.07533 3.30954i 0.0819935 0.252350i
\(173\) 0.804337 + 2.47549i 0.0611526 + 0.188208i 0.976966 0.213396i \(-0.0684526\pi\)
−0.915813 + 0.401605i \(0.868453\pi\)
\(174\) 0 0
\(175\) 14.6543 1.10776
\(176\) 1.34445 4.95097i 0.101342 0.373194i
\(177\) 0 0
\(178\) 8.64378 6.28007i 0.647878 0.470711i
\(179\) −2.34483 7.21663i −0.175261 0.539396i 0.824385 0.566030i \(-0.191521\pi\)
−0.999645 + 0.0266334i \(0.991521\pi\)
\(180\) 0 0
\(181\) 1.94179 + 1.41080i 0.144332 + 0.104864i 0.657608 0.753360i \(-0.271568\pi\)
−0.513276 + 0.858224i \(0.671568\pi\)
\(182\) 5.61975 + 4.08298i 0.416563 + 0.302651i
\(183\) 0 0
\(184\) 1.54465 + 4.75396i 0.113873 + 0.350466i
\(185\) −7.86453 + 5.71392i −0.578212 + 0.420095i
\(186\) 0 0
\(187\) −4.82087 + 17.7530i −0.352537 + 1.29823i
\(188\) 20.0064 1.45911
\(189\) 0 0
\(190\) 1.17647 + 3.62081i 0.0853504 + 0.262681i
\(191\) 5.10442 15.7098i 0.369343 1.13672i −0.577874 0.816126i \(-0.696118\pi\)
0.947217 0.320594i \(-0.103882\pi\)
\(192\) 0 0
\(193\) 6.58132 + 4.78161i 0.473734 + 0.344188i 0.798895 0.601471i \(-0.205418\pi\)
−0.325161 + 0.945659i \(0.605418\pi\)
\(194\) 1.64550 5.06434i 0.118140 0.363598i
\(195\) 0 0
\(196\) 10.3975 7.55422i 0.742678 0.539587i
\(197\) 22.9072 1.63207 0.816035 0.578003i \(-0.196168\pi\)
0.816035 + 0.578003i \(0.196168\pi\)
\(198\) 0 0
\(199\) 9.27177 0.657259 0.328629 0.944459i \(-0.393413\pi\)
0.328629 + 0.944459i \(0.393413\pi\)
\(200\) −7.17828 + 5.21532i −0.507581 + 0.368779i
\(201\) 0 0
\(202\) −0.361574 + 1.11281i −0.0254402 + 0.0782970i
\(203\) −3.42115 2.48561i −0.240118 0.174456i
\(204\) 0 0
\(205\) −1.00724 + 3.09998i −0.0703489 + 0.216512i
\(206\) 0.551741 + 1.69808i 0.0384416 + 0.118311i
\(207\) 0 0
\(208\) 4.14243 0.287226
\(209\) 13.2645 10.6678i 0.917527 0.737909i
\(210\) 0 0
\(211\) −3.40643 + 2.47491i −0.234508 + 0.170380i −0.698833 0.715285i \(-0.746297\pi\)
0.464325 + 0.885665i \(0.346297\pi\)
\(212\) 2.71712 + 8.36244i 0.186613 + 0.574335i
\(213\) 0 0
\(214\) −5.52301 4.01270i −0.377545 0.274303i
\(215\) −2.01683 1.46531i −0.137547 0.0999334i
\(216\) 0 0
\(217\) 0.519021 + 1.59738i 0.0352335 + 0.108437i
\(218\) −1.26990 + 0.922637i −0.0860086 + 0.0624889i
\(219\) 0 0
\(220\) −4.83059 3.16014i −0.325678 0.213057i
\(221\) −14.8537 −0.999170
\(222\) 0 0
\(223\) −2.11957 6.52335i −0.141937 0.436836i 0.854668 0.519175i \(-0.173761\pi\)
−0.996604 + 0.0823393i \(0.973761\pi\)
\(224\) −6.94477 + 21.3738i −0.464017 + 1.42810i
\(225\) 0 0
\(226\) 0.823601 + 0.598381i 0.0547851 + 0.0398037i
\(227\) −8.69262 + 26.7531i −0.576950 + 1.77567i 0.0524933 + 0.998621i \(0.483283\pi\)
−0.629443 + 0.777047i \(0.716717\pi\)
\(228\) 0 0
\(229\) 11.3543 8.24939i 0.750314 0.545135i −0.145610 0.989342i \(-0.546515\pi\)
0.895924 + 0.444207i \(0.146515\pi\)
\(230\) 1.56844 0.103420
\(231\) 0 0
\(232\) 2.56042 0.168100
\(233\) −11.7385 + 8.52854i −0.769017 + 0.558723i −0.901663 0.432440i \(-0.857653\pi\)
0.132646 + 0.991163i \(0.457653\pi\)
\(234\) 0 0
\(235\) 4.42895 13.6309i 0.288913 0.889182i
\(236\) 2.99534 + 2.17624i 0.194980 + 0.141661i
\(237\) 0 0
\(238\) 4.44585 13.6829i 0.288181 0.886931i
\(239\) 7.77120 + 23.9173i 0.502677 + 1.54708i 0.804641 + 0.593762i \(0.202358\pi\)
−0.301964 + 0.953319i \(0.597642\pi\)
\(240\) 0 0
\(241\) 17.7422 1.14288 0.571438 0.820645i \(-0.306386\pi\)
0.571438 + 0.820645i \(0.306386\pi\)
\(242\) 1.56731 7.13747i 0.100750 0.458814i
\(243\) 0 0
\(244\) −5.15048 + 3.74205i −0.329726 + 0.239560i
\(245\) −2.84514 8.75643i −0.181769 0.559428i
\(246\) 0 0
\(247\) 11.1195 + 8.07877i 0.707515 + 0.514040i
\(248\) −0.822729 0.597747i −0.0522433 0.0379570i
\(249\) 0 0
\(250\) 2.00646 + 6.17526i 0.126900 + 0.390558i
\(251\) −17.6993 + 12.8593i −1.11717 + 0.811670i −0.983777 0.179394i \(-0.942586\pi\)
−0.133390 + 0.991064i \(0.542586\pi\)
\(252\) 0 0
\(253\) −2.49108 6.55523i −0.156613 0.412124i
\(254\) −5.08294 −0.318932
\(255\) 0 0
\(256\) −2.71480 8.35529i −0.169675 0.522205i
\(257\) −1.59568 + 4.91099i −0.0995356 + 0.306339i −0.988409 0.151814i \(-0.951489\pi\)
0.888874 + 0.458153i \(0.151489\pi\)
\(258\) 0 0
\(259\) −27.5002 19.9801i −1.70878 1.24150i
\(260\) 1.44031 4.43283i 0.0893244 0.274912i
\(261\) 0 0
\(262\) −2.88024 + 2.09262i −0.177942 + 0.129282i
\(263\) 27.8981 1.72027 0.860135 0.510066i \(-0.170379\pi\)
0.860135 + 0.510066i \(0.170379\pi\)
\(264\) 0 0
\(265\) 6.29908 0.386949
\(266\) −10.7701 + 7.82496i −0.660359 + 0.479779i
\(267\) 0 0
\(268\) 4.69698 14.4558i 0.286914 0.883029i
\(269\) 2.44290 + 1.77487i 0.148946 + 0.108216i 0.659763 0.751474i \(-0.270657\pi\)
−0.510816 + 0.859690i \(0.670657\pi\)
\(270\) 0 0
\(271\) −7.84125 + 24.1329i −0.476322 + 1.46597i 0.367845 + 0.929887i \(0.380096\pi\)
−0.844167 + 0.536081i \(0.819904\pi\)
\(272\) −2.65125 8.15971i −0.160756 0.494755i
\(273\) 0 0
\(274\) −11.1149 −0.671474
\(275\) 9.70002 7.80111i 0.584933 0.470425i
\(276\) 0 0
\(277\) 8.54677 6.20959i 0.513525 0.373098i −0.300634 0.953740i \(-0.597198\pi\)
0.814159 + 0.580642i \(0.197198\pi\)
\(278\) 2.82066 + 8.68109i 0.169172 + 0.520657i
\(279\) 0 0
\(280\) 8.33875 + 6.05845i 0.498335 + 0.362062i
\(281\) −18.2599 13.2666i −1.08930 0.791420i −0.110016 0.993930i \(-0.535090\pi\)
−0.979280 + 0.202510i \(0.935090\pi\)
\(282\) 0 0
\(283\) −1.81616 5.58958i −0.107960 0.332266i 0.882454 0.470399i \(-0.155890\pi\)
−0.990414 + 0.138133i \(0.955890\pi\)
\(284\) −7.96581 + 5.78750i −0.472684 + 0.343425i
\(285\) 0 0
\(286\) 5.89337 0.289010i 0.348482 0.0170895i
\(287\) −11.3977 −0.672782
\(288\) 0 0
\(289\) 4.25344 + 13.0907i 0.250202 + 0.770044i
\(290\) 0.248263 0.764074i 0.0145785 0.0448680i
\(291\) 0 0
\(292\) −14.7192 10.6941i −0.861376 0.625827i
\(293\) −2.19220 + 6.74690i −0.128070 + 0.394158i −0.994448 0.105230i \(-0.966442\pi\)
0.866378 + 0.499389i \(0.166442\pi\)
\(294\) 0 0
\(295\) 2.14583 1.55904i 0.124935 0.0907707i
\(296\) 20.5814 1.19627
\(297\) 0 0
\(298\) −3.69339 −0.213953
\(299\) 4.58091 3.32822i 0.264921 0.192476i
\(300\) 0 0
\(301\) 2.69375 8.29051i 0.155265 0.477857i
\(302\) 0.0880915 + 0.0640022i 0.00506910 + 0.00368292i
\(303\) 0 0
\(304\) −2.45325 + 7.55033i −0.140704 + 0.433041i
\(305\) 1.40936 + 4.33757i 0.0806999 + 0.248369i
\(306\) 0 0
\(307\) −18.5370 −1.05796 −0.528981 0.848633i \(-0.677426\pi\)
−0.528981 + 0.848633i \(0.677426\pi\)
\(308\) 5.28966 19.4793i 0.301406 1.10994i
\(309\) 0 0
\(310\) −0.258151 + 0.187558i −0.0146620 + 0.0106526i
\(311\) −2.12487 6.53969i −0.120491 0.370832i 0.872562 0.488503i \(-0.162457\pi\)
−0.993053 + 0.117672i \(0.962457\pi\)
\(312\) 0 0
\(313\) 20.4890 + 14.8861i 1.15811 + 0.841414i 0.989537 0.144276i \(-0.0460853\pi\)
0.168569 + 0.985690i \(0.446085\pi\)
\(314\) −12.8197 9.31407i −0.723459 0.525624i
\(315\) 0 0
\(316\) −2.17455 6.69256i −0.122328 0.376486i
\(317\) 8.88241 6.45345i 0.498886 0.362462i −0.309705 0.950833i \(-0.600230\pi\)
0.808591 + 0.588371i \(0.200230\pi\)
\(318\) 0 0
\(319\) −3.58773 + 0.175942i −0.200874 + 0.00985083i
\(320\) −0.815165 −0.0455691
\(321\) 0 0
\(322\) 1.69478 + 5.21599i 0.0944463 + 0.290676i
\(323\) 8.79675 27.0736i 0.489464 1.50642i
\(324\) 0 0
\(325\) 8.13140 + 5.90780i 0.451049 + 0.327706i
\(326\) −0.861386 + 2.65107i −0.0477078 + 0.146829i
\(327\) 0 0
\(328\) 5.58302 4.05630i 0.308271 0.223972i
\(329\) 50.1166 2.76302
\(330\) 0 0
\(331\) −3.71025 −0.203934 −0.101967 0.994788i \(-0.532514\pi\)
−0.101967 + 0.994788i \(0.532514\pi\)
\(332\) −0.607805 + 0.441596i −0.0333576 + 0.0242357i
\(333\) 0 0
\(334\) −3.25182 + 10.0081i −0.177931 + 0.547617i
\(335\) −8.80935 6.40037i −0.481306 0.349690i
\(336\) 0 0
\(337\) −9.94885 + 30.6194i −0.541948 + 1.66795i 0.186189 + 0.982514i \(0.440386\pi\)
−0.728137 + 0.685432i \(0.759614\pi\)
\(338\) −1.19647 3.68235i −0.0650793 0.200294i
\(339\) 0 0
\(340\) −9.65356 −0.523538
\(341\) 1.19390 + 0.781045i 0.0646535 + 0.0422960i
\(342\) 0 0
\(343\) 3.93417 2.85834i 0.212425 0.154336i
\(344\) 1.63100 + 5.01970i 0.0879375 + 0.270644i
\(345\) 0 0
\(346\) −1.39891 1.01637i −0.0752061 0.0546404i
\(347\) −17.4121 12.6506i −0.934728 0.679120i 0.0124177 0.999923i \(-0.496047\pi\)
−0.947146 + 0.320803i \(0.896047\pi\)
\(348\) 0 0
\(349\) −5.19765 15.9967i −0.278224 0.856285i −0.988348 0.152209i \(-0.951361\pi\)
0.710124 0.704076i \(-0.248639\pi\)
\(350\) −7.87593 + 5.72219i −0.420986 + 0.305864i
\(351\) 0 0
\(352\) 6.78127 + 17.8448i 0.361443 + 0.951129i
\(353\) −3.13085 −0.166639 −0.0833193 0.996523i \(-0.526552\pi\)
−0.0833193 + 0.996523i \(0.526552\pi\)
\(354\) 0 0
\(355\) 2.17974 + 6.70855i 0.115689 + 0.356053i
\(356\) 7.74653 23.8414i 0.410565 1.26359i
\(357\) 0 0
\(358\) 4.07815 + 2.96295i 0.215537 + 0.156597i
\(359\) −2.62315 + 8.07323i −0.138445 + 0.426089i −0.996110 0.0881197i \(-0.971914\pi\)
0.857665 + 0.514208i \(0.171914\pi\)
\(360\) 0 0
\(361\) −5.93893 + 4.31489i −0.312575 + 0.227099i
\(362\) −1.59449 −0.0838048
\(363\) 0 0
\(364\) 16.2981 0.854254
\(365\) −10.5447 + 7.66118i −0.551935 + 0.401004i
\(366\) 0 0
\(367\) −3.40258 + 10.4720i −0.177613 + 0.546637i −0.999743 0.0226630i \(-0.992786\pi\)
0.822130 + 0.569300i \(0.192786\pi\)
\(368\) 2.64596 + 1.92241i 0.137930 + 0.100212i
\(369\) 0 0
\(370\) 1.99561 6.14185i 0.103747 0.319300i
\(371\) 6.80648 + 20.9482i 0.353375 + 1.08758i
\(372\) 0 0
\(373\) 11.0068 0.569912 0.284956 0.958541i \(-0.408021\pi\)
0.284956 + 0.958541i \(0.408021\pi\)
\(374\) −4.34118 11.4237i −0.224477 0.590706i
\(375\) 0 0
\(376\) −24.5491 + 17.8360i −1.26602 + 0.919820i
\(377\) −0.896269 2.75843i −0.0461602 0.142067i
\(378\) 0 0
\(379\) −20.5384 14.9220i −1.05499 0.766492i −0.0818315 0.996646i \(-0.526077\pi\)
−0.973154 + 0.230154i \(0.926077\pi\)
\(380\) 7.22664 + 5.25046i 0.370719 + 0.269343i
\(381\) 0 0
\(382\) 3.39097 + 10.4363i 0.173497 + 0.533969i
\(383\) −9.80103 + 7.12086i −0.500809 + 0.363859i −0.809326 0.587360i \(-0.800167\pi\)
0.308517 + 0.951219i \(0.400167\pi\)
\(384\) 0 0
\(385\) −12.1008 7.91626i −0.616713 0.403450i
\(386\) −5.40422 −0.275068
\(387\) 0 0
\(388\) −3.86080 11.8823i −0.196003 0.603234i
\(389\) −4.43473 + 13.6487i −0.224850 + 0.692016i 0.773457 + 0.633849i \(0.218526\pi\)
−0.998307 + 0.0581676i \(0.981474\pi\)
\(390\) 0 0
\(391\) −9.48778 6.89328i −0.479818 0.348608i
\(392\) −6.02370 + 18.5390i −0.304243 + 0.936362i
\(393\) 0 0
\(394\) −12.3114 + 8.94475i −0.620239 + 0.450630i
\(395\) −5.04123 −0.253652
\(396\) 0 0
\(397\) −5.03882 −0.252891 −0.126446 0.991974i \(-0.540357\pi\)
−0.126446 + 0.991974i \(0.540357\pi\)
\(398\) −4.98308 + 3.62042i −0.249779 + 0.181475i
\(399\) 0 0
\(400\) −1.79400 + 5.52136i −0.0897000 + 0.276068i
\(401\) −14.7243 10.6978i −0.735294 0.534223i 0.155940 0.987767i \(-0.450159\pi\)
−0.891234 + 0.453544i \(0.850159\pi\)
\(402\) 0 0
\(403\) −0.355980 + 1.09560i −0.0177327 + 0.0545755i
\(404\) 0.848352 + 2.61096i 0.0422071 + 0.129900i
\(405\) 0 0
\(406\) 2.80926 0.139421
\(407\) −28.8392 + 1.41427i −1.42951 + 0.0701027i
\(408\) 0 0
\(409\) −13.2925 + 9.65758i −0.657273 + 0.477537i −0.865741 0.500493i \(-0.833152\pi\)
0.208468 + 0.978029i \(0.433152\pi\)
\(410\) −0.669133 2.05938i −0.0330461 0.101705i
\(411\) 0 0
\(412\) 3.38914 + 2.46235i 0.166971 + 0.121311i
\(413\) 7.50342 + 5.45155i 0.369219 + 0.268253i
\(414\) 0 0
\(415\) 0.166318 + 0.511874i 0.00816423 + 0.0251269i
\(416\) −12.4702 + 9.06015i −0.611403 + 0.444211i
\(417\) 0 0
\(418\) −2.96343 + 10.9129i −0.144946 + 0.533767i
\(419\) 17.4065 0.850362 0.425181 0.905108i \(-0.360210\pi\)
0.425181 + 0.905108i \(0.360210\pi\)
\(420\) 0 0
\(421\) 1.40561 + 4.32602i 0.0685052 + 0.210837i 0.979449 0.201694i \(-0.0646447\pi\)
−0.910943 + 0.412531i \(0.864645\pi\)
\(422\) 0.864374 2.66027i 0.0420771 0.129500i
\(423\) 0 0
\(424\) −10.7893 7.83890i −0.523976 0.380691i
\(425\) 6.43284 19.7983i 0.312039 0.960356i
\(426\) 0 0
\(427\) −12.9021 + 9.37395i −0.624378 + 0.453637i
\(428\) −16.0176 −0.774239
\(429\) 0 0
\(430\) 1.65611 0.0798647
\(431\) 10.1004 7.33838i 0.486520 0.353477i −0.317325 0.948317i \(-0.602784\pi\)
0.803844 + 0.594840i \(0.202784\pi\)
\(432\) 0 0
\(433\) 8.86451 27.2822i 0.426001 1.31110i −0.476031 0.879428i \(-0.657925\pi\)
0.902032 0.431668i \(-0.142075\pi\)
\(434\) −0.902689 0.655842i −0.0433304 0.0314814i
\(435\) 0 0
\(436\) −1.13808 + 3.50266i −0.0545042 + 0.167747i
\(437\) 3.35336 + 10.3206i 0.160413 + 0.493701i
\(438\) 0 0
\(439\) −4.10807 −0.196068 −0.0980338 0.995183i \(-0.531255\pi\)
−0.0980338 + 0.995183i \(0.531255\pi\)
\(440\) 8.74476 0.428841i 0.416890 0.0204442i
\(441\) 0 0
\(442\) 7.98309 5.80005i 0.379717 0.275880i
\(443\) 6.56034 + 20.1906i 0.311691 + 0.959287i 0.977095 + 0.212803i \(0.0682593\pi\)
−0.665404 + 0.746483i \(0.731741\pi\)
\(444\) 0 0
\(445\) −14.5289 10.5559i −0.688736 0.500396i
\(446\) 3.68638 + 2.67831i 0.174555 + 0.126822i
\(447\) 0 0
\(448\) −0.880828 2.71091i −0.0416152 0.128078i
\(449\) 20.9494 15.2206i 0.988663 0.718306i 0.0290350 0.999578i \(-0.490757\pi\)
0.959628 + 0.281273i \(0.0907566\pi\)
\(450\) 0 0
\(451\) −7.54435 + 6.06744i −0.355249 + 0.285705i
\(452\) 2.38857 0.112349
\(453\) 0 0
\(454\) −5.77469 17.7727i −0.271019 0.834112i
\(455\) 3.60803 11.1044i 0.169147 0.520581i
\(456\) 0 0
\(457\) 8.33600 + 6.05645i 0.389941 + 0.283309i 0.765431 0.643517i \(-0.222526\pi\)
−0.375490 + 0.926826i \(0.622526\pi\)
\(458\) −2.88113 + 8.86721i −0.134626 + 0.414338i
\(459\) 0 0
\(460\) 2.97717 2.16304i 0.138811 0.100852i
\(461\) 25.4532 1.18548 0.592738 0.805395i \(-0.298047\pi\)
0.592738 + 0.805395i \(0.298047\pi\)
\(462\) 0 0
\(463\) −39.8554 −1.85224 −0.926119 0.377231i \(-0.876876\pi\)
−0.926119 + 0.377231i \(0.876876\pi\)
\(464\) 1.35533 0.984708i 0.0629198 0.0457139i
\(465\) 0 0
\(466\) 2.97863 9.16727i 0.137982 0.424666i
\(467\) −14.0582 10.2139i −0.650537 0.472643i 0.212917 0.977070i \(-0.431704\pi\)
−0.863454 + 0.504427i \(0.831704\pi\)
\(468\) 0 0
\(469\) 11.7661 36.2123i 0.543308 1.67213i
\(470\) 2.94224 + 9.05529i 0.135716 + 0.417689i
\(471\) 0 0
\(472\) −5.61562 −0.258480
\(473\) −2.63033 6.92165i −0.120943 0.318258i
\(474\) 0 0
\(475\) −15.5837 + 11.3222i −0.715027 + 0.519498i
\(476\) −10.4312 32.1039i −0.478112 1.47148i
\(477\) 0 0
\(478\) −13.5158 9.81979i −0.618197 0.449147i
\(479\) −17.7142 12.8701i −0.809383 0.588051i 0.104269 0.994549i \(-0.466750\pi\)
−0.913652 + 0.406498i \(0.866750\pi\)
\(480\) 0 0
\(481\) −7.20447 22.1731i −0.328496 1.01101i
\(482\) −9.53548 + 6.92794i −0.434329 + 0.315559i
\(483\) 0 0
\(484\) −6.86830 15.7097i −0.312195 0.714075i
\(485\) −8.95046 −0.406420
\(486\) 0 0
\(487\) 1.01084 + 3.11106i 0.0458057 + 0.140975i 0.971344 0.237679i \(-0.0763867\pi\)
−0.925538 + 0.378655i \(0.876387\pi\)
\(488\) 2.98389 9.18347i 0.135074 0.415716i
\(489\) 0 0
\(490\) 4.94830 + 3.59515i 0.223542 + 0.162412i
\(491\) 2.23231 6.87034i 0.100743 0.310054i −0.887965 0.459911i \(-0.847881\pi\)
0.988708 + 0.149857i \(0.0478813\pi\)
\(492\) 0 0
\(493\) −4.85989 + 3.53092i −0.218879 + 0.159025i
\(494\) −9.13071 −0.410810
\(495\) 0 0
\(496\) −0.665390 −0.0298769
\(497\) −19.9546 + 14.4979i −0.895087 + 0.650319i
\(498\) 0 0
\(499\) 4.58412 14.1085i 0.205213 0.631581i −0.794491 0.607275i \(-0.792262\pi\)
0.999705 0.0243059i \(-0.00773756\pi\)
\(500\) 12.3250 + 8.95460i 0.551189 + 0.400462i
\(501\) 0 0
\(502\) 4.49115 13.8223i 0.200450 0.616921i
\(503\) 10.1918 + 31.3671i 0.454430 + 1.39859i 0.871803 + 0.489856i \(0.162951\pi\)
−0.417374 + 0.908735i \(0.637049\pi\)
\(504\) 0 0
\(505\) 1.96673 0.0875181
\(506\) 3.89850 + 2.55037i 0.173309 + 0.113378i
\(507\) 0 0
\(508\) −9.64831 + 7.00990i −0.428074 + 0.311014i
\(509\) −11.9495 36.7768i −0.529652 1.63010i −0.754929 0.655807i \(-0.772329\pi\)
0.225277 0.974295i \(-0.427671\pi\)
\(510\) 0 0
\(511\) −36.8721 26.7892i −1.63113 1.18508i
\(512\) −13.1198 9.53213i −0.579821 0.421264i
\(513\) 0 0
\(514\) −1.06004 3.26247i −0.0467564 0.143901i
\(515\) 2.42795 1.76401i 0.106988 0.0777315i
\(516\) 0 0
\(517\) 33.1733 26.6792i 1.45896 1.17335i
\(518\) 22.5817 0.992182
\(519\) 0 0
\(520\) 2.18457 + 6.72343i 0.0957999 + 0.294842i
\(521\) 5.40297 16.6286i 0.236708 0.728514i −0.760182 0.649710i \(-0.774890\pi\)
0.996890 0.0788032i \(-0.0251099\pi\)
\(522\) 0 0
\(523\) −11.7211 8.51591i −0.512530 0.372375i 0.301253 0.953544i \(-0.402595\pi\)
−0.813782 + 0.581170i \(0.802595\pi\)
\(524\) −2.58126 + 7.94431i −0.112763 + 0.347049i
\(525\) 0 0
\(526\) −14.9937 + 10.8936i −0.653758 + 0.474983i
\(527\) 2.38593 0.103933
\(528\) 0 0
\(529\) −18.5294 −0.805626
\(530\) −3.38542 + 2.45965i −0.147053 + 0.106840i
\(531\) 0 0
\(532\) −9.65216 + 29.7063i −0.418474 + 1.28793i
\(533\) −6.32433 4.59489i −0.273937 0.199027i
\(534\) 0 0
\(535\) −3.54592 + 10.9132i −0.153304 + 0.471820i
\(536\) 7.12408 + 21.9256i 0.307713 + 0.947044i
\(537\) 0 0
\(538\) −2.00597 −0.0864837
\(539\) 7.16664 26.3913i 0.308689 1.13675i
\(540\) 0 0
\(541\) −26.7771 + 19.4547i −1.15124 + 0.836422i −0.988645 0.150272i \(-0.951985\pi\)
−0.162591 + 0.986694i \(0.551985\pi\)
\(542\) −5.20910 16.0320i −0.223750 0.688632i
\(543\) 0 0
\(544\) 25.8278 + 18.7650i 1.10736 + 0.804543i
\(545\) 2.13451 + 1.55082i 0.0914325 + 0.0664296i
\(546\) 0 0
\(547\) 2.84732 + 8.76316i 0.121743 + 0.374686i 0.993294 0.115619i \(-0.0368853\pi\)
−0.871551 + 0.490305i \(0.836885\pi\)
\(548\) −21.0980 + 15.3286i −0.901262 + 0.654805i
\(549\) 0 0
\(550\) −2.16708 + 7.98032i −0.0924046 + 0.340282i
\(551\) 5.55853 0.236802
\(552\) 0 0
\(553\) −5.44731 16.7651i −0.231643 0.712925i
\(554\) −2.16872 + 6.67464i −0.0921402 + 0.283578i
\(555\) 0 0
\(556\) 17.3262 + 12.5883i 0.734796 + 0.533861i
\(557\) −11.4496 + 35.2384i −0.485137 + 1.49310i 0.346645 + 0.937996i \(0.387321\pi\)
−0.831782 + 0.555102i \(0.812679\pi\)
\(558\) 0 0
\(559\) 4.83697 3.51427i 0.204582 0.148638i
\(560\) 6.74405 0.284988
\(561\) 0 0
\(562\) 14.9941 0.632486
\(563\) −21.8387 + 15.8667i −0.920390 + 0.668702i −0.943621 0.331028i \(-0.892605\pi\)
0.0232313 + 0.999730i \(0.492605\pi\)
\(564\) 0 0
\(565\) 0.528774 1.62740i 0.0222457 0.0684652i
\(566\) 3.15870 + 2.29493i 0.132770 + 0.0964630i
\(567\) 0 0
\(568\) 4.61492 14.2033i 0.193638 0.595956i
\(569\) 8.49046 + 26.1310i 0.355939 + 1.09547i 0.955463 + 0.295110i \(0.0953564\pi\)
−0.599524 + 0.800356i \(0.704644\pi\)
\(570\) 0 0
\(571\) −39.0103 −1.63253 −0.816266 0.577676i \(-0.803960\pi\)
−0.816266 + 0.577676i \(0.803960\pi\)
\(572\) 10.7881 8.67617i 0.451072 0.362769i
\(573\) 0 0
\(574\) 6.12563 4.45053i 0.255679 0.185762i
\(575\) 2.45223 + 7.54719i 0.102265 + 0.314739i
\(576\) 0 0
\(577\) 23.5957 + 17.1433i 0.982302 + 0.713684i 0.958222 0.286026i \(-0.0923344\pi\)
0.0240800 + 0.999710i \(0.492334\pi\)
\(578\) −7.39764 5.37470i −0.307701 0.223558i
\(579\) 0 0
\(580\) −0.582493 1.79273i −0.0241867 0.0744390i
\(581\) −1.52257 + 1.10621i −0.0631670 + 0.0458935i
\(582\) 0 0
\(583\) 15.6569 + 10.2427i 0.648445 + 0.424209i
\(584\) 27.5954 1.14191
\(585\) 0 0
\(586\) −1.45632 4.48210i −0.0601602 0.185154i
\(587\) 1.57226 4.83891i 0.0648940 0.199723i −0.913352 0.407170i \(-0.866516\pi\)
0.978246 + 0.207447i \(0.0665155\pi\)
\(588\) 0 0
\(589\) −1.78610 1.29768i −0.0735950 0.0534699i
\(590\) −0.544500 + 1.67580i −0.0224167 + 0.0689916i
\(591\) 0 0
\(592\) 10.8946 7.91537i 0.447764 0.325320i
\(593\) −3.46422 −0.142258 −0.0711292 0.997467i \(-0.522660\pi\)
−0.0711292 + 0.997467i \(0.522660\pi\)
\(594\) 0 0
\(595\) −24.1825 −0.991386
\(596\) −7.01071 + 5.09358i −0.287170 + 0.208641i
\(597\) 0 0
\(598\) −1.16240 + 3.57748i −0.0475339 + 0.146294i
\(599\) 20.1242 + 14.6211i 0.822251 + 0.597400i 0.917356 0.398067i \(-0.130319\pi\)
−0.0951054 + 0.995467i \(0.530319\pi\)
\(600\) 0 0
\(601\) 3.42024 10.5264i 0.139514 0.429381i −0.856750 0.515731i \(-0.827520\pi\)
0.996265 + 0.0863500i \(0.0275203\pi\)
\(602\) 1.78951 + 5.50755i 0.0729351 + 0.224471i
\(603\) 0 0
\(604\) 0.255479 0.0103953
\(605\) −12.2239 + 1.20181i −0.496973 + 0.0488604i
\(606\) 0 0
\(607\) 22.6209 16.4351i 0.918155 0.667079i −0.0249090 0.999690i \(-0.507930\pi\)
0.943064 + 0.332611i \(0.107930\pi\)
\(608\) −9.12859 28.0949i −0.370213 1.13940i
\(609\) 0 0
\(610\) −2.45118 1.78089i −0.0992455 0.0721061i
\(611\) 27.8087 + 20.2042i 1.12502 + 0.817375i
\(612\) 0 0
\(613\) 3.39680 + 10.4543i 0.137196 + 0.422245i 0.995925 0.0901845i \(-0.0287457\pi\)
−0.858729 + 0.512429i \(0.828746\pi\)
\(614\) 9.96265 7.23829i 0.402060 0.292114i
\(615\) 0 0
\(616\) 10.8753 + 28.6182i 0.438179 + 1.15306i
\(617\) −18.6262 −0.749864 −0.374932 0.927052i \(-0.622334\pi\)
−0.374932 + 0.927052i \(0.622334\pi\)
\(618\) 0 0
\(619\) 0.830787 + 2.55690i 0.0333921 + 0.102770i 0.966363 0.257180i \(-0.0827935\pi\)
−0.932971 + 0.359951i \(0.882793\pi\)
\(620\) −0.231355 + 0.712036i −0.00929142 + 0.0285961i
\(621\) 0 0
\(622\) 3.69561 + 2.68502i 0.148180 + 0.107659i
\(623\) 19.4053 59.7234i 0.777457 2.39277i
\(624\) 0 0
\(625\) −6.35233 + 4.61524i −0.254093 + 0.184610i
\(626\) −16.8244 −0.672440
\(627\) 0 0
\(628\) −37.1792 −1.48361
\(629\) −39.0652 + 28.3826i −1.55763 + 1.13169i
\(630\) 0 0
\(631\) −12.1224 + 37.3089i −0.482585 + 1.48524i 0.352863 + 0.935675i \(0.385208\pi\)
−0.835448 + 0.549569i \(0.814792\pi\)
\(632\) 8.63483 + 6.27357i 0.343475 + 0.249549i
\(633\) 0 0
\(634\) −2.25389 + 6.93677i −0.0895135 + 0.275494i
\(635\) 2.64013 + 8.12550i 0.104771 + 0.322451i
\(636\) 0 0
\(637\) 22.0813 0.874895
\(638\) 1.85951 1.49549i 0.0736187 0.0592069i
\(639\) 0 0
\(640\) −9.96109 + 7.23716i −0.393747 + 0.286074i
\(641\) −7.95687 24.4887i −0.314277 0.967246i −0.976051 0.217542i \(-0.930196\pi\)
0.661773 0.749704i \(-0.269804\pi\)
\(642\) 0 0
\(643\) 10.7859 + 7.83639i 0.425353 + 0.309037i 0.779788 0.626044i \(-0.215327\pi\)
−0.354435 + 0.935081i \(0.615327\pi\)
\(644\) 10.4104 + 7.56359i 0.410227 + 0.298047i
\(645\) 0 0
\(646\) 5.84386 + 17.9856i 0.229924 + 0.707632i
\(647\) 19.2955 14.0190i 0.758585 0.551145i −0.139891 0.990167i \(-0.544675\pi\)
0.898476 + 0.439022i \(0.144675\pi\)
\(648\) 0 0
\(649\) 7.86876 0.385882i 0.308876 0.0151472i
\(650\) −6.67706 −0.261896
\(651\) 0 0
\(652\) 2.02105 + 6.22015i 0.0791504 + 0.243600i
\(653\) −3.93222 + 12.1021i −0.153880 + 0.473593i −0.998046 0.0624889i \(-0.980096\pi\)
0.844166 + 0.536082i \(0.180096\pi\)
\(654\) 0 0
\(655\) 4.84125 + 3.51738i 0.189163 + 0.137435i
\(656\) 1.39531 4.29433i 0.0544778 0.167666i
\(657\) 0 0
\(658\) −26.9350 + 19.5694i −1.05004 + 0.762896i
\(659\) 27.2527 1.06161 0.530806 0.847493i \(-0.321889\pi\)
0.530806 + 0.847493i \(0.321889\pi\)
\(660\) 0 0
\(661\) 43.6440 1.69755 0.848777 0.528751i \(-0.177339\pi\)
0.848777 + 0.528751i \(0.177339\pi\)
\(662\) 1.99406 1.44877i 0.0775014 0.0563081i
\(663\) 0 0
\(664\) 0.352127 1.08373i 0.0136652 0.0420571i
\(665\) 18.1030 + 13.1526i 0.702003 + 0.510035i
\(666\) 0 0
\(667\) 0.707636 2.17788i 0.0273998 0.0843278i
\(668\) 7.62965 + 23.4817i 0.295200 + 0.908533i
\(669\) 0 0
\(670\) 7.23376 0.279465
\(671\) −3.55005 + 13.0732i −0.137048 + 0.504684i
\(672\) 0 0
\(673\) 21.5900 15.6860i 0.832233 0.604652i −0.0879575 0.996124i \(-0.528034\pi\)
0.920190 + 0.391472i \(0.128034\pi\)
\(674\) −6.60922 20.3411i −0.254578 0.783510i
\(675\) 0 0
\(676\) −7.34946 5.33970i −0.282672 0.205373i
\(677\) 21.9107 + 15.9190i 0.842095 + 0.611818i 0.922955 0.384908i \(-0.125767\pi\)
−0.0808602 + 0.996725i \(0.525767\pi\)
\(678\) 0 0
\(679\) −9.67144 29.7656i −0.371156 1.14230i
\(680\) 11.8455 8.60629i 0.454256 0.330036i
\(681\) 0 0
\(682\) −0.946640 + 0.0464231i −0.0362487 + 0.00177763i
\(683\) 16.7343 0.640322 0.320161 0.947363i \(-0.396263\pi\)
0.320161 + 0.947363i \(0.396263\pi\)
\(684\) 0 0
\(685\) 5.77319 + 17.7681i 0.220582 + 0.678883i
\(686\) −0.998288 + 3.07242i −0.0381148 + 0.117305i
\(687\) 0 0
\(688\) 2.79387 + 2.02987i 0.106515 + 0.0773879i
\(689\) −4.66836 + 14.3677i −0.177850 + 0.547367i
\(690\) 0 0
\(691\) 30.3540 22.0534i 1.15472 0.838953i 0.165618 0.986190i \(-0.447038\pi\)
0.989101 + 0.147237i \(0.0470381\pi\)
\(692\) −4.05707 −0.154226
\(693\) 0 0
\(694\) 14.2978 0.542738
\(695\) 12.4124 9.01811i 0.470828 0.342077i
\(696\) 0 0
\(697\) −5.00325 + 15.3984i −0.189512 + 0.583257i
\(698\) 9.03983 + 6.56782i 0.342163 + 0.248596i
\(699\) 0 0
\(700\) −7.05838 + 21.7235i −0.266782 + 0.821070i
\(701\) −3.15219 9.70143i −0.119056 0.366418i 0.873715 0.486438i \(-0.161704\pi\)
−0.992771 + 0.120020i \(0.961704\pi\)
\(702\) 0 0
\(703\) 44.6811 1.68518
\(704\) −2.02617 1.32551i −0.0763641 0.0499569i
\(705\) 0 0
\(706\) 1.68267 1.22253i 0.0633280 0.0460105i
\(707\) 2.12515 + 6.54054i 0.0799245 + 0.245982i
\(708\) 0 0
\(709\) 11.7289 + 8.52152i 0.440487 + 0.320032i 0.785828 0.618445i \(-0.212237\pi\)
−0.345342 + 0.938477i \(0.612237\pi\)
\(710\) −3.79104 2.75435i −0.142275 0.103369i
\(711\) 0 0
\(712\) 11.7494 + 36.1610i 0.440329 + 1.35519i
\(713\) −0.735822 + 0.534606i −0.0275568 + 0.0200212i
\(714\) 0 0
\(715\) −3.52309 9.27093i −0.131756 0.346713i
\(716\) 11.8273 0.442006
\(717\) 0 0
\(718\) −1.74261 5.36321i −0.0650337 0.200153i
\(719\) −5.94135 + 18.2856i −0.221575 + 0.681938i 0.777046 + 0.629444i \(0.216717\pi\)
−0.998621 + 0.0524943i \(0.983283\pi\)
\(720\) 0 0
\(721\) 8.48991 + 6.16828i 0.316181 + 0.229719i
\(722\) 1.50699 4.63804i 0.0560844 0.172610i
\(723\) 0 0
\(724\) −3.02663 + 2.19898i −0.112484 + 0.0817243i
\(725\) 4.06482 0.150964
\(726\) 0 0
\(727\) 0.726827 0.0269565 0.0134783 0.999909i \(-0.495710\pi\)
0.0134783 + 0.999909i \(0.495710\pi\)
\(728\) −19.9989 + 14.5300i −0.741207 + 0.538519i
\(729\) 0 0
\(730\) 2.67570 8.23495i 0.0990320 0.304789i
\(731\) −10.0181 7.27860i −0.370534 0.269209i
\(732\) 0 0
\(733\) −0.579681 + 1.78408i −0.0214110 + 0.0658964i −0.961191 0.275883i \(-0.911030\pi\)
0.939780 + 0.341780i \(0.111030\pi\)
\(734\) −2.26040 6.95680i −0.0834329 0.256780i
\(735\) 0 0
\(736\) −12.1699 −0.448590
\(737\) −11.4891 30.2333i −0.423206 1.11366i
\(738\) 0 0
\(739\) 42.5402 30.9073i 1.56487 1.13694i 0.632993 0.774157i \(-0.281826\pi\)
0.931873 0.362784i \(-0.118174\pi\)
\(740\) −4.68224 14.4105i −0.172123 0.529739i
\(741\) 0 0
\(742\) −11.8379 8.60076i −0.434584 0.315744i
\(743\) −26.9668 19.5925i −0.989316 0.718780i −0.0295450 0.999563i \(-0.509406\pi\)
−0.959771 + 0.280783i \(0.909406\pi\)
\(744\) 0 0
\(745\) 1.91839 + 5.90420i 0.0702844 + 0.216313i
\(746\) −5.91558 + 4.29792i −0.216585 + 0.157358i
\(747\) 0 0
\(748\) −23.9948 15.6973i −0.877338 0.573949i
\(749\) −40.1246 −1.46612
\(750\) 0 0
\(751\) −7.21990 22.2206i −0.263458 0.810840i −0.992045 0.125886i \(-0.959823\pi\)
0.728587 0.684953i \(-0.240177\pi\)
\(752\) −6.13533 + 18.8826i −0.223732 + 0.688578i
\(753\) 0 0
\(754\) 1.55880 + 1.13254i 0.0567683 + 0.0412446i
\(755\) 0.0565572 0.174065i 0.00205833 0.00633488i
\(756\) 0 0
\(757\) 27.3472 19.8689i 0.993952 0.722148i 0.0331687 0.999450i \(-0.489440\pi\)
0.960783 + 0.277302i \(0.0894401\pi\)
\(758\) 16.8650 0.612564
\(759\) 0 0
\(760\) −13.5484 −0.491453
\(761\) 16.2709 11.8215i 0.589819 0.428528i −0.252432 0.967615i \(-0.581230\pi\)
0.842251 + 0.539086i \(0.181230\pi\)
\(762\) 0 0
\(763\) −2.85093 + 8.77427i −0.103211 + 0.317650i
\(764\) 20.8294 + 15.1335i 0.753583 + 0.547510i
\(765\) 0 0
\(766\) 2.48699 7.65417i 0.0898586 0.276556i
\(767\) 1.96573 + 6.04991i 0.0709786 + 0.218450i
\(768\) 0 0
\(769\) 0.626999 0.0226102 0.0113051 0.999936i \(-0.496401\pi\)
0.0113051 + 0.999936i \(0.496401\pi\)
\(770\) 9.59465 0.470520i 0.345767 0.0169564i
\(771\) 0 0
\(772\) −10.2582 + 7.45299i −0.369199 + 0.268239i
\(773\) −8.88046 27.3313i −0.319408 0.983037i −0.973902 0.226970i \(-0.927118\pi\)
0.654494 0.756067i \(-0.272882\pi\)
\(774\) 0 0
\(775\) −1.30613 0.948959i −0.0469176 0.0340876i
\(776\) 15.3307 + 11.1384i 0.550341 + 0.399846i
\(777\) 0 0
\(778\) −2.94608 9.06711i −0.105622 0.325072i
\(779\) 12.1204 8.80602i 0.434260 0.315508i
\(780\) 0 0
\(781\) −5.49056 + 20.2191i −0.196468 + 0.723497i
\(782\) 7.79085 0.278600
\(783\) 0 0
\(784\) 3.94131 + 12.1301i 0.140761 + 0.433218i
\(785\) −8.23062 + 25.3312i −0.293763 + 0.904110i
\(786\) 0 0
\(787\) 11.4095 + 8.28950i 0.406705 + 0.295489i 0.772267 0.635298i \(-0.219123\pi\)
−0.365561 + 0.930787i \(0.619123\pi\)
\(788\) −11.0334 + 33.9574i −0.393050 + 1.20968i
\(789\) 0 0
\(790\) 2.70939 1.96849i 0.0963958 0.0700357i
\(791\) 5.98345 0.212747
\(792\) 0 0
\(793\) −10.9382 −0.388426
\(794\) 2.70810 1.96755i 0.0961068 0.0698257i
\(795\) 0 0
\(796\) −4.46582 + 13.7444i −0.158287 + 0.487157i
\(797\) 21.1596 + 15.3733i 0.749511 + 0.544552i 0.895675 0.444709i \(-0.146693\pi\)
−0.146164 + 0.989260i \(0.546693\pi\)
\(798\) 0 0
\(799\) 21.9998 67.7084i 0.778297 2.39535i
\(800\) −6.67551 20.5451i −0.236015 0.726379i
\(801\) 0 0
\(802\) 12.0908 0.426939
\(803\) −38.6674 + 1.89624i −1.36454 + 0.0669169i
\(804\) 0 0
\(805\) 7.45791 5.41849i 0.262857 0.190977i
\(806\) −0.236485 0.727826i −0.00832983 0.0256366i
\(807\) 0 0
\(808\) −3.36869 2.44750i −0.118510 0.0861026i
\(809\) 12.8256 + 9.31836i 0.450925 + 0.327616i 0.789961 0.613157i \(-0.210101\pi\)
−0.339036 + 0.940773i \(0.610101\pi\)
\(810\) 0 0
\(811\) −11.2255 34.5484i −0.394179 1.21316i −0.929599 0.368573i \(-0.879846\pi\)
0.535420 0.844586i \(-0.320154\pi\)
\(812\) 5.33248 3.87427i 0.187133 0.135960i
\(813\) 0 0
\(814\) 14.9473 12.0212i 0.523902 0.421342i
\(815\) 4.68538 0.164122
\(816\) 0 0
\(817\) 3.54081 + 10.8975i 0.123877 + 0.381255i
\(818\) 3.37295 10.3809i 0.117932 0.362958i
\(819\) 0 0
\(820\) −4.11023 2.98626i −0.143535 0.104285i
\(821\) 5.05451 15.5562i 0.176404 0.542914i −0.823291 0.567619i \(-0.807865\pi\)
0.999695 + 0.0247048i \(0.00786458\pi\)
\(822\) 0 0
\(823\) 21.1756 15.3850i 0.738136 0.536287i −0.153991 0.988072i \(-0.549213\pi\)
0.892127 + 0.451785i \(0.149213\pi\)
\(824\) −6.35392 −0.221349
\(825\) 0 0
\(826\) −6.16139 −0.214382
\(827\) 4.48139 3.25592i 0.155833 0.113219i −0.507136 0.861866i \(-0.669296\pi\)
0.662969 + 0.748647i \(0.269296\pi\)
\(828\) 0 0
\(829\) 5.71784 17.5977i 0.198589 0.611194i −0.801327 0.598227i \(-0.795872\pi\)
0.999916 0.0129672i \(-0.00412771\pi\)
\(830\) −0.289263 0.210162i −0.0100405 0.00729481i
\(831\) 0 0
\(832\) 0.604133 1.85933i 0.0209445 0.0644606i
\(833\) −14.1326 43.4956i −0.489664 1.50703i
\(834\) 0 0
\(835\) 17.6878 0.612110
\(836\) 9.42492 + 24.8015i 0.325968 + 0.857776i
\(837\) 0 0
\(838\) −9.35505 + 6.79684i −0.323165 + 0.234793i
\(839\) 5.55158 + 17.0860i 0.191662 + 0.589875i 0.999999 + 0.00115518i \(0.000367705\pi\)
−0.808337 + 0.588719i \(0.799632\pi\)
\(840\) 0 0
\(841\) 22.5125 + 16.3563i 0.776294 + 0.564011i
\(842\) −2.44465 1.77614i −0.0842483 0.0612100i
\(843\) 0 0
\(844\) −2.02806 6.24172i −0.0698086 0.214849i
\(845\) −5.26509 + 3.82531i −0.181125 + 0.131595i
\(846\) 0 0
\(847\) −17.2053 39.3532i −0.591182 1.35219i
\(848\) −8.72598 −0.299651
\(849\) 0 0
\(850\) 4.27347 + 13.1524i 0.146579 + 0.451123i
\(851\) 5.68818 17.5064i 0.194988 0.600112i
\(852\) 0 0
\(853\) −22.5822 16.4069i −0.773199 0.561762i 0.129732 0.991549i \(-0.458588\pi\)
−0.902930 + 0.429788i \(0.858588\pi\)
\(854\) 3.27389 10.0760i 0.112030 0.344794i
\(855\) 0 0
\(856\) 19.6546 14.2799i 0.671781 0.488077i
\(857\) 8.49967 0.290343 0.145172 0.989406i \(-0.453627\pi\)
0.145172 + 0.989406i \(0.453627\pi\)
\(858\) 0 0
\(859\) 27.8517 0.950289 0.475145 0.879908i \(-0.342396\pi\)
0.475145 + 0.879908i \(0.342396\pi\)
\(860\) 3.14359 2.28395i 0.107195 0.0778820i
\(861\) 0 0
\(862\) −2.56296 + 7.88797i −0.0872947 + 0.268665i
\(863\) 10.9978 + 7.99035i 0.374368 + 0.271995i 0.759020 0.651067i \(-0.225678\pi\)
−0.384652 + 0.923062i \(0.625678\pi\)
\(864\) 0 0
\(865\) −0.898141 + 2.76419i −0.0305377 + 0.0939854i
\(866\) 5.88887 + 18.1241i 0.200112 + 0.615882i
\(867\) 0 0
\(868\) −2.61794 −0.0888586
\(869\) −12.5304 8.19734i −0.425066 0.278076i
\(870\) 0 0
\(871\) 21.1275 15.3500i 0.715879 0.520117i
\(872\) −1.72617 5.31260i −0.0584555 0.179907i
\(873\) 0 0
\(874\) −5.83221 4.23735i −0.197278 0.143331i
\(875\) 30.8744 + 22.4316i 1.04375 + 0.758326i
\(876\) 0 0
\(877\) 11.1796 + 34.4073i 0.377509 + 1.16185i 0.941771 + 0.336256i \(0.109161\pi\)
−0.564262 + 0.825596i \(0.690839\pi\)
\(878\) 2.20787 1.60411i 0.0745120 0.0541361i
\(879\) 0 0
\(880\) 4.46403 3.59014i 0.150482 0.121023i
\(881\) −26.6423 −0.897601 −0.448800 0.893632i \(-0.648149\pi\)
−0.448800 + 0.893632i \(0.648149\pi\)
\(882\) 0 0
\(883\) −6.32757 19.4743i −0.212940 0.655361i −0.999293 0.0375844i \(-0.988034\pi\)
0.786354 0.617776i \(-0.211966\pi\)
\(884\) 7.15442 22.0190i 0.240629 0.740581i
\(885\) 0 0
\(886\) −11.4098 8.28973i −0.383321 0.278499i
\(887\) 9.88890 30.4349i 0.332037 1.02190i −0.636126 0.771585i \(-0.719464\pi\)
0.968163 0.250320i \(-0.0805357\pi\)
\(888\) 0 0
\(889\) −24.1693 + 17.5600i −0.810613 + 0.588945i
\(890\) 11.9303 0.399906
\(891\) 0 0
\(892\) 10.6911 0.357963
\(893\) −53.2948 + 38.7209i −1.78344 + 1.29575i
\(894\) 0 0
\(895\) 2.61829 8.05826i 0.0875197 0.269358i
\(896\) −34.8314 25.3065i −1.16363 0.845430i
\(897\) 0 0
\(898\) −5.31586 + 16.3605i −0.177393 + 0.545958i
\(899\) 0.143966 + 0.443082i 0.00480153 + 0.0147776i
\(900\) 0 0
\(901\) 31.2892 1.04239
\(902\) 1.68548 6.20683i 0.0561204 0.206665i
\(903\) 0 0
\(904\) −2.93093 + 2.12944i −0.0974813 + 0.0708243i
\(905\) 0.828198 + 2.54893i 0.0275302 + 0.0847294i
\(906\) 0 0
\(907\) 39.6825 + 28.8310i 1.31764 + 0.957318i 0.999958 + 0.00911935i \(0.00290282\pi\)
0.317677 + 0.948199i \(0.397097\pi\)
\(908\) −35.4717 25.7717i −1.17717 0.855265i
\(909\) 0 0
\(910\) 2.39689 + 7.37687i 0.0794561 + 0.244541i
\(911\) −18.9159 + 13.7432i −0.626710 + 0.455332i −0.855259 0.518201i \(-0.826602\pi\)
0.228549 + 0.973532i \(0.426602\pi\)
\(912\) 0 0
\(913\) −0.418940 + 1.54275i −0.0138649 + 0.0510577i
\(914\) −6.84506 −0.226415
\(915\) 0 0
\(916\) 6.75993 + 20.8049i 0.223354 + 0.687414i
\(917\) −6.46615 + 19.9008i −0.213531 + 0.657181i
\(918\) 0 0
\(919\) 6.14797 + 4.46676i 0.202803 + 0.147345i 0.684551 0.728965i \(-0.259998\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(920\) −1.72480 + 5.30838i −0.0568649 + 0.175012i
\(921\) 0 0
\(922\) −13.6798 + 9.93893i −0.450519 + 0.327321i
\(923\) −16.9171 −0.556835
\(924\) 0 0
\(925\) 32.6742 1.07432
\(926\) 21.4202 15.5627i 0.703910 0.511421i
\(927\) 0 0
\(928\) −1.92634 + 5.92866i −0.0632352 + 0.194618i
\(929\) −12.0355 8.74433i −0.394873 0.286892i 0.372576 0.928002i \(-0.378475\pi\)
−0.767450 + 0.641109i \(0.778475\pi\)
\(930\) 0 0
\(931\) −13.0771 + 40.2472i −0.428585 + 1.31905i
\(932\) −6.98867 21.5089i −0.228922 0.704548i
\(933\) 0 0
\(934\) 11.5438 0.377726
\(935\) −16.0069 + 12.8733i −0.523482 + 0.421003i
\(936\) 0 0
\(937\) −14.4192 + 10.4762i −0.471056 + 0.342242i −0.797853 0.602853i \(-0.794031\pi\)
0.326797 + 0.945095i \(0.394031\pi\)
\(938\) 7.81646 + 24.0566i 0.255216 + 0.785475i
\(939\) 0 0
\(940\) 18.0731 + 13.1309i 0.589479 + 0.428282i
\(941\) 34.5120 + 25.0744i 1.12506 + 0.817402i 0.984968 0.172737i \(-0.0552609\pi\)
0.140090 + 0.990139i \(0.455261\pi\)
\(942\) 0 0
\(943\) −1.90726 5.86995i −0.0621090 0.191152i
\(944\) −2.97257 + 2.15970i −0.0967491 + 0.0702923i
\(945\) 0 0
\(946\) 4.11641 + 2.69293i 0.133836 + 0.0875548i
\(947\) −6.89340 −0.224006 −0.112003 0.993708i \(-0.535727\pi\)
−0.112003 + 0.993708i \(0.535727\pi\)
\(948\) 0 0
\(949\) −9.65971 29.7295i −0.313567 0.965061i
\(950\) 3.95432 12.1701i 0.128295 0.394852i
\(951\) 0 0
\(952\) 41.4208 + 30.0940i 1.34246 + 0.975351i
\(953\) 7.31766 22.5214i 0.237042 0.729541i −0.759802 0.650155i \(-0.774704\pi\)
0.996844 0.0793863i \(-0.0252960\pi\)
\(954\) 0 0
\(955\) 14.9220 10.8415i 0.482866 0.350822i
\(956\) −39.1978 −1.26775
\(957\) 0 0
\(958\) 14.5459 0.469958
\(959\) −52.8512 + 38.3986i −1.70665 + 1.23996i
\(960\) 0 0
\(961\) −9.52235 + 29.3068i −0.307172 + 0.945380i
\(962\) 12.5301 + 9.10366i 0.403987 + 0.293514i
\(963\) 0 0
\(964\) −8.54567 + 26.3009i −0.275238 + 0.847094i
\(965\) 2.80701 + 8.63910i 0.0903610 + 0.278102i
\(966\) 0 0
\(967\) −31.1399 −1.00139 −0.500696 0.865623i \(-0.666923\pi\)
−0.500696 + 0.865623i \(0.666923\pi\)
\(968\) 22.4332 + 13.1536i 0.721032 + 0.422772i
\(969\) 0 0
\(970\) 4.81040 3.49496i 0.154453 0.112216i
\(971\) −4.12687 12.7012i −0.132438 0.407601i 0.862745 0.505639i \(-0.168743\pi\)
−0.995183 + 0.0980383i \(0.968743\pi\)
\(972\) 0 0
\(973\) 43.4028 + 31.5340i 1.39143 + 1.01093i
\(974\) −1.75807 1.27732i −0.0563323 0.0409278i
\(975\) 0 0
\(976\) −1.95236 6.00875i −0.0624936 0.192335i
\(977\) −7.21314 + 5.24065i −0.230769 + 0.167663i −0.697161 0.716915i \(-0.745554\pi\)
0.466392 + 0.884578i \(0.345554\pi\)
\(978\) 0 0
\(979\) −18.9485 49.8624i −0.605595 1.59361i
\(980\) 14.3508 0.458421
\(981\) 0 0
\(982\) 1.48297 + 4.56411i 0.0473234 + 0.145647i
\(983\) 5.20958 16.0334i 0.166160 0.511387i −0.832960 0.553333i \(-0.813356\pi\)
0.999120 + 0.0419459i \(0.0133557\pi\)
\(984\) 0 0
\(985\) 20.6936 + 15.0348i 0.659353 + 0.479048i
\(986\) 1.23319 3.79536i 0.0392727 0.120869i
\(987\) 0 0
\(988\) −17.3317 + 12.5922i −0.551394 + 0.400612i
\(989\) 4.72049 0.150103
\(990\) 0 0
\(991\) −33.5356 −1.06529 −0.532647 0.846338i \(-0.678803\pi\)
−0.532647 + 0.846338i \(0.678803\pi\)
\(992\) 2.00307 1.45531i 0.0635975 0.0462063i
\(993\) 0 0
\(994\) 5.06344 15.5837i 0.160603 0.494284i
\(995\) 8.37582 + 6.08539i 0.265531 + 0.192920i
\(996\) 0 0
\(997\) −1.00235 + 3.08492i −0.0317447 + 0.0977003i −0.965673 0.259759i \(-0.916357\pi\)
0.933929 + 0.357459i \(0.116357\pi\)
\(998\) 3.04532 + 9.37254i 0.0963980 + 0.296682i
\(999\) 0 0
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 891.2.f.e.487.4 36
3.2 odd 2 891.2.f.f.487.6 36
9.2 odd 6 99.2.m.b.58.4 yes 72
9.4 even 3 297.2.n.b.289.4 72
9.5 odd 6 99.2.m.b.25.6 yes 72
9.7 even 3 297.2.n.b.91.6 72
11.2 odd 10 9801.2.a.cn.1.8 18
11.4 even 5 inner 891.2.f.e.730.4 36
11.9 even 5 9801.2.a.cp.1.11 18
33.2 even 10 9801.2.a.co.1.11 18
33.20 odd 10 9801.2.a.cm.1.8 18
33.26 odd 10 891.2.f.f.730.6 36
99.2 even 30 1089.2.e.o.364.8 36
99.4 even 15 297.2.n.b.235.6 72
99.20 odd 30 1089.2.e.p.364.11 36
99.59 odd 30 99.2.m.b.70.4 yes 72
99.68 even 30 1089.2.e.o.727.8 36
99.70 even 15 297.2.n.b.37.4 72
99.86 odd 30 1089.2.e.p.727.11 36
99.92 odd 30 99.2.m.b.4.6 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.6 72 99.92 odd 30
99.2.m.b.25.6 yes 72 9.5 odd 6
99.2.m.b.58.4 yes 72 9.2 odd 6
99.2.m.b.70.4 yes 72 99.59 odd 30
297.2.n.b.37.4 72 99.70 even 15
297.2.n.b.91.6 72 9.7 even 3
297.2.n.b.235.6 72 99.4 even 15
297.2.n.b.289.4 72 9.4 even 3
891.2.f.e.487.4 36 1.1 even 1 trivial
891.2.f.e.730.4 36 11.4 even 5 inner
891.2.f.f.487.6 36 3.2 odd 2
891.2.f.f.730.6 36 33.26 odd 10
1089.2.e.o.364.8 36 99.2 even 30
1089.2.e.o.727.8 36 99.68 even 30
1089.2.e.p.364.11 36 99.20 odd 30
1089.2.e.p.727.11 36 99.86 odd 30
9801.2.a.cm.1.8 18 33.20 odd 10
9801.2.a.cn.1.8 18 11.2 odd 10
9801.2.a.co.1.11 18 33.2 even 10
9801.2.a.cp.1.11 18 11.9 even 5