Properties

Label 891.2.f.e.730.4
Level $891$
Weight $2$
Character 891.730
Analytic conductor $7.115$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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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 730.4
Character \(\chi\) \(=\) 891.730
Dual form 891.2.f.e.487.4

$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

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

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 0.381327 0.924440i \(-0.375467\pi\)
−0.761359 + 0.648331i \(0.775467\pi\)
\(3\) 0 0
\(4\) −0.481658 1.48239i −0.240829 0.741196i
\(5\) 0.903367 0.656335i 0.403998 0.293522i −0.367169 0.930154i \(-0.619673\pi\)
0.771168 + 0.636632i \(0.219673\pi\)
\(6\) 0 0
\(7\) −1.20657 3.71344i −0.456041 1.40355i −0.869909 0.493212i \(-0.835823\pi\)
0.413869 0.910337i \(-0.364177\pi\)
\(8\) −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 0.245303 0.969447i \(-0.421113\pi\)
−0.846196 + 0.532872i \(0.821113\pi\)
\(14\) −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 0.109207 0.994019i \(-0.465169\pi\)
0.979115 + 0.203306i \(0.0651688\pi\)
\(18\) 0 0
\(19\) −1.58598 + 4.88115i −0.363849 + 1.11981i 0.586850 + 0.809696i \(0.300368\pi\)
−0.950699 + 0.310116i \(0.899632\pi\)
\(20\) −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 0.915162 0.403087i \(-0.132063\pi\)
−0.977310 + 0.211814i \(0.932063\pi\)
\(30\) 0 0
\(31\) 0.348009 + 0.252843i 0.0625042 + 0.0454120i 0.618599 0.785707i \(-0.287701\pi\)
−0.556094 + 0.831119i \(0.687701\pi\)
\(32\) 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 −0.885447 0.464740i \(-0.846148\pi\)
0.443175 0.896435i \(-0.353852\pi\)
\(38\) 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 −0.855582 0.517667i \(-0.826800\pi\)
0.996458 + 0.0840968i \(0.0268005\pi\)
\(42\) 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 0.0451833 + 0.998979i \(0.485613\pi\)
−0.623739 + 0.781633i \(0.714387\pi\)
\(48\) 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 0.855321 0.518099i \(-0.173360\pi\)
−0.228433 + 0.973560i \(0.573360\pi\)
\(54\) 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 0.987400 0.158245i \(-0.0505836\pi\)
−0.891837 + 0.452356i \(0.850584\pi\)
\(60\) 0 0
\(61\) 3.30439 2.40078i 0.423084 0.307389i −0.355793 0.934565i \(-0.615789\pi\)
0.778878 + 0.627176i \(0.215789\pi\)
\(62\) −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 −0.241668 0.970359i \(-0.577694\pi\)
0.848187 + 0.529697i \(0.177694\pi\)
\(72\) 0 0
\(73\) −3.60705 11.1014i −0.422174 1.29932i −0.905675 0.423973i \(-0.860635\pi\)
0.483501 0.875344i \(-0.339365\pi\)
\(74\) −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 0.363045 0.931772i \(-0.381737\pi\)
−0.773980 + 0.633209i \(0.781737\pi\)
\(80\) −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 −0.566178 0.824283i \(-0.691579\pi\)
0.608981 + 0.793185i \(0.291579\pi\)
\(84\) 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 0.207701 0.978192i \(-0.433402\pi\)
−0.866133 + 0.499814i \(0.833402\pi\)
\(98\) 5.47762 0.553323
\(99\) 0 0
\(100\) 5.84996 0.584996
\(101\) 1.42493 + 1.03527i 0.141786 + 0.103014i 0.656417 0.754398i \(-0.272071\pi\)
−0.514631 + 0.857412i \(0.672071\pi\)
\(102\) 0 0
\(103\) 0.830534 + 2.55612i 0.0818350 + 0.251862i 0.983600 0.180365i \(-0.0577279\pi\)
−0.901765 + 0.432227i \(0.857728\pi\)
\(104\) 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 −0.671931 0.740614i \(-0.734535\pi\)
0.978925 0.204219i \(-0.0654653\pi\)
\(108\) 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 −0.970857 0.239661i \(-0.922964\pi\)
0.926309 + 0.376765i \(0.122964\pi\)
\(114\) 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 −0.278241 0.960511i \(-0.589751\pi\)
0.827519 + 0.561437i \(0.189751\pi\)
\(128\) −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 0.167119 0.985937i \(-0.446554\pi\)
0.989324 + 0.145731i \(0.0465535\pi\)
\(138\) 0 0
\(139\) 4.24593 + 13.0676i 0.360135 + 1.10838i 0.952972 + 0.303059i \(0.0980079\pi\)
−0.592837 + 0.805323i \(0.701992\pi\)
\(140\) −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 −0.388101 0.921617i \(-0.626869\pi\)
0.756580 + 0.653901i \(0.226869\pi\)
\(150\) 0 0
\(151\) −0.0506502 + 0.155885i −0.00412186 + 0.0126858i −0.953096 0.302667i \(-0.902123\pi\)
0.948974 + 0.315353i \(0.102123\pi\)
\(152\) −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 0.00254199 0.999997i \(-0.499191\pi\)
0.585727 0.810509i \(-0.300809\pi\)
\(158\) 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 0.712740 0.701429i \(-0.247454\pi\)
−0.446850 + 0.894609i \(0.647454\pi\)
\(164\) −4.54990 −0.355288
\(165\) 0 0
\(166\) −0.320205 −0.0248527
\(167\) 12.8151 + 9.31075i 0.991666 + 0.720488i 0.960285 0.279020i \(-0.0900096\pi\)
0.0313807 + 0.999508i \(0.490010\pi\)
\(168\) 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 −0.915813 0.401605i \(-0.868453\pi\)
0.976966 + 0.213396i \(0.0684526\pi\)
\(174\) 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 −0.999645 0.0266334i \(-0.991521\pi\)
0.824385 + 0.566030i \(0.191521\pi\)
\(180\) 0 0
\(181\) 1.94179 1.41080i 0.144332 0.104864i −0.513276 0.858224i \(-0.671568\pi\)
0.657608 + 0.753360i \(0.271568\pi\)
\(182\) 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 0.947217 + 0.320594i \(0.103882\pi\)
−0.577874 + 0.816126i \(0.696118\pi\)
\(192\) 0 0
\(193\) 6.58132 4.78161i 0.473734 0.344188i −0.325161 0.945659i \(-0.605418\pi\)
0.798895 + 0.601471i \(0.205418\pi\)
\(194\) 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 0.464325 0.885665i \(-0.346297\pi\)
−0.698833 + 0.715285i \(0.746297\pi\)
\(212\) 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 −0.996604 0.0823393i \(-0.973761\pi\)
0.854668 + 0.519175i \(0.173761\pi\)
\(224\) −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 −0.629443 0.777047i \(-0.716717\pi\)
0.0524933 0.998621i \(-0.483283\pi\)
\(228\) 0 0
\(229\) 11.3543 + 8.24939i 0.750314 + 0.545135i 0.895924 0.444207i \(-0.146515\pi\)
−0.145610 + 0.989342i \(0.546515\pi\)
\(230\) 1.56844 0.103420
\(231\) 0 0
\(232\) 2.56042 0.168100
\(233\) −11.7385 8.52854i −0.769017 0.558723i 0.132646 0.991163i \(-0.457653\pi\)
−0.901663 + 0.432440i \(0.857653\pi\)
\(234\) 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 −0.301964 0.953319i \(-0.597642\pi\)
0.804641 0.593762i \(-0.202358\pi\)
\(240\) 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 −0.133390 0.991064i \(-0.542586\pi\)
−0.983777 + 0.179394i \(0.942586\pi\)
\(252\) 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 0.888874 0.458153i \(-0.151489\pi\)
−0.988409 + 0.151814i \(0.951489\pi\)
\(258\) 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 −0.510816 0.859690i \(-0.670657\pi\)
0.659763 + 0.751474i \(0.270657\pi\)
\(270\) 0 0
\(271\) −7.84125 24.1329i −0.476322 1.46597i −0.844167 0.536081i \(-0.819904\pi\)
0.367845 0.929887i \(-0.380096\pi\)
\(272\) −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 0.814159 0.580642i \(-0.197198\pi\)
−0.300634 + 0.953740i \(0.597198\pi\)
\(278\) 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 −0.979280 0.202510i \(-0.935090\pi\)
−0.110016 + 0.993930i \(0.535090\pi\)
\(282\) 0 0
\(283\) −1.81616 + 5.58958i −0.107960 + 0.332266i −0.990414 0.138133i \(-0.955890\pi\)
0.882454 + 0.470399i \(0.155890\pi\)
\(284\) −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 0.866378 0.499389i \(-0.166442\pi\)
−0.994448 + 0.105230i \(0.966442\pi\)
\(294\) 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 −0.993053 0.117672i \(-0.962457\pi\)
0.872562 + 0.488503i \(0.162457\pi\)
\(312\) 0 0
\(313\) 20.4890 14.8861i 1.15811 0.841414i 0.168569 0.985690i \(-0.446085\pi\)
0.989537 + 0.144276i \(0.0460853\pi\)
\(314\) −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 0.808591 0.588371i \(-0.200230\pi\)
−0.309705 + 0.950833i \(0.600230\pi\)
\(318\) 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 −0.728137 0.685432i \(-0.759614\pi\)
0.186189 0.982514i \(-0.440386\pi\)
\(338\) −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 −0.947146 0.320803i \(-0.896047\pi\)
0.0124177 + 0.999923i \(0.496047\pi\)
\(348\) 0 0
\(349\) −5.19765 + 15.9967i −0.278224 + 0.856285i 0.710124 + 0.704076i \(0.248639\pi\)
−0.988348 + 0.152209i \(0.951361\pi\)
\(350\) −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 0.857665 0.514208i \(-0.171914\pi\)
−0.996110 + 0.0881197i \(0.971914\pi\)
\(360\) 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 0.822130 0.569300i \(-0.192786\pi\)
−0.999743 + 0.0226630i \(0.992786\pi\)
\(368\) 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 −0.973154 0.230154i \(-0.926077\pi\)
−0.0818315 + 0.996646i \(0.526077\pi\)
\(380\) 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 0.308517 0.951219i \(-0.400167\pi\)
−0.809326 + 0.587360i \(0.800167\pi\)
\(384\) 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 −0.998307 0.0581676i \(-0.981474\pi\)
0.773457 0.633849i \(-0.218526\pi\)
\(390\) 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 −0.891234 0.453544i \(-0.850159\pi\)
0.155940 + 0.987767i \(0.450159\pi\)
\(402\) 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 0.208468 0.978029i \(-0.433152\pi\)
−0.865741 + 0.500493i \(0.833152\pi\)
\(410\) −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 −0.910943 0.412531i \(-0.864645\pi\)
0.979449 + 0.201694i \(0.0646447\pi\)
\(422\) 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 0.803844 0.594840i \(-0.202784\pi\)
−0.317325 + 0.948317i \(0.602784\pi\)
\(432\) 0 0
\(433\) 8.86451 + 27.2822i 0.426001 + 1.31110i 0.902032 + 0.431668i \(0.142075\pi\)
−0.476031 + 0.879428i \(0.657925\pi\)
\(434\) −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 −0.665404 0.746483i \(-0.731741\pi\)
0.977095 0.212803i \(-0.0682593\pi\)
\(444\) 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 0.959628 0.281273i \(-0.0907566\pi\)
0.0290350 + 0.999578i \(0.490757\pi\)
\(450\) 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 −0.375490 0.926826i \(-0.622526\pi\)
0.765431 + 0.643517i \(0.222526\pi\)
\(458\) −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 −0.863454 0.504427i \(-0.831704\pi\)
0.212917 + 0.977070i \(0.431704\pi\)
\(468\) 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 −0.913652 0.406498i \(-0.866750\pi\)
0.104269 + 0.994549i \(0.466750\pi\)
\(480\) 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 −0.925538 0.378655i \(-0.876387\pi\)
0.971344 + 0.237679i \(0.0763867\pi\)
\(488\) 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 0.988708 0.149857i \(-0.0478813\pi\)
−0.887965 + 0.459911i \(0.847881\pi\)
\(492\) 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 0.999705 + 0.0243059i \(0.00773756\pi\)
−0.794491 + 0.607275i \(0.792262\pi\)
\(500\) 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 −0.417374 0.908735i \(-0.637049\pi\)
0.871803 0.489856i \(-0.162951\pi\)
\(504\) 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 0.225277 + 0.974295i \(0.427671\pi\)
−0.754929 + 0.655807i \(0.772329\pi\)
\(510\) 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 0.996890 + 0.0788032i \(0.0251099\pi\)
−0.760182 + 0.649710i \(0.774890\pi\)
\(522\) 0 0
\(523\) −11.7211 + 8.51591i −0.512530 + 0.372375i −0.813782 0.581170i \(-0.802595\pi\)
0.301253 + 0.953544i \(0.402595\pi\)
\(524\) −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 −0.162591 0.986694i \(-0.551985\pi\)
−0.988645 + 0.150272i \(0.951985\pi\)
\(542\) −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 −0.871551 0.490305i \(-0.836885\pi\)
0.993294 + 0.115619i \(0.0368853\pi\)
\(548\) −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 −0.831782 0.555102i \(-0.812679\pi\)
0.346645 0.937996i \(-0.387321\pi\)
\(558\) 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 0.0232313 0.999730i \(-0.492605\pi\)
−0.943621 + 0.331028i \(0.892605\pi\)
\(564\) 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 −0.599524 0.800356i \(-0.704644\pi\)
0.955463 0.295110i \(-0.0953564\pi\)
\(570\) 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 0.0240800 0.999710i \(-0.492334\pi\)
0.958222 + 0.286026i \(0.0923344\pi\)
\(578\) −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 0.978246 0.207447i \(-0.0665155\pi\)
−0.913352 + 0.407170i \(0.866516\pi\)
\(588\) 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 −0.0951054 0.995467i \(-0.530319\pi\)
0.917356 + 0.398067i \(0.130319\pi\)
\(600\) 0 0
\(601\) 3.42024 + 10.5264i 0.139514 + 0.429381i 0.996265 0.0863500i \(-0.0275203\pi\)
−0.856750 + 0.515731i \(0.827520\pi\)
\(602\) 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 0.943064 0.332611i \(-0.107930\pi\)
−0.0249090 + 0.999690i \(0.507930\pi\)
\(608\) −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 −0.858729 0.512429i \(-0.828746\pi\)
0.995925 + 0.0901845i \(0.0287457\pi\)
\(614\) 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 −0.932971 0.359951i \(-0.882793\pi\)
0.966363 + 0.257180i \(0.0827935\pi\)
\(620\) −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 −0.835448 0.549569i \(-0.814792\pi\)
0.352863 0.935675i \(-0.385208\pi\)
\(632\) 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 0.661773 + 0.749704i \(0.269804\pi\)
−0.976051 + 0.217542i \(0.930196\pi\)
\(642\) 0 0
\(643\) 10.7859 7.83639i 0.425353 0.309037i −0.354435 0.935081i \(-0.615327\pi\)
0.779788 + 0.626044i \(0.215327\pi\)
\(644\) 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 0.898476 0.439022i \(-0.144675\pi\)
−0.139891 + 0.990167i \(0.544675\pi\)
\(648\) 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 0.844166 0.536082i \(-0.180096\pi\)
−0.998046 + 0.0624889i \(0.980096\pi\)
\(654\) 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 0.920190 0.391472i \(-0.128034\pi\)
−0.0879575 + 0.996124i \(0.528034\pi\)
\(674\) −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 −0.0808602 0.996725i \(-0.525767\pi\)
0.922955 + 0.384908i \(0.125767\pi\)
\(678\) 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 0.989101 0.147237i \(-0.0470381\pi\)
0.165618 + 0.986190i \(0.447038\pi\)
\(692\) −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 −0.992771 0.120020i \(-0.961704\pi\)
0.873715 + 0.486438i \(0.161704\pi\)
\(702\) 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 −0.345342 0.938477i \(-0.612237\pi\)
0.785828 + 0.618445i \(0.212237\pi\)
\(710\) −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 −0.998621 0.0524943i \(-0.983283\pi\)
0.777046 0.629444i \(-0.216717\pi\)
\(720\) 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 0.939780 0.341780i \(-0.111030\pi\)
−0.961191 + 0.275883i \(0.911030\pi\)
\(734\) −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 0.931873 + 0.362784i \(0.118174\pi\)
0.632993 + 0.774157i \(0.281826\pi\)
\(740\) −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 −0.959771 0.280783i \(-0.909406\pi\)
−0.0295450 + 0.999563i \(0.509406\pi\)
\(744\) 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 0.728587 + 0.684953i \(0.240177\pi\)
−0.992045 + 0.125886i \(0.959823\pi\)
\(752\) −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 0.960783 0.277302i \(-0.0894401\pi\)
0.0331687 + 0.999450i \(0.489440\pi\)
\(758\) 16.8650 0.612564
\(759\) 0 0
\(760\) −13.5484 −0.491453
\(761\) 16.2709 + 11.8215i 0.589819 + 0.428528i 0.842251 0.539086i \(-0.181230\pi\)
−0.252432 + 0.967615i \(0.581230\pi\)
\(762\) 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 0.654494 + 0.756067i \(0.272882\pi\)
−0.973902 + 0.226970i \(0.927118\pi\)
\(774\) 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 −0.365561 0.930787i \(-0.619123\pi\)
0.772267 + 0.635298i \(0.219123\pi\)
\(788\) −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 −0.146164 0.989260i \(-0.546693\pi\)
0.895675 + 0.444709i \(0.146693\pi\)
\(798\) 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 −0.339036 0.940773i \(-0.610101\pi\)
0.789961 + 0.613157i \(0.210101\pi\)
\(810\) 0 0
\(811\) −11.2255 + 34.5484i −0.394179 + 1.21316i 0.535420 + 0.844586i \(0.320154\pi\)
−0.929599 + 0.368573i \(0.879846\pi\)
\(812\) 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 0.999695 0.0247048i \(-0.00786458\pi\)
−0.823291 + 0.567619i \(0.807865\pi\)
\(822\) 0 0
\(823\) 21.1756 + 15.3850i 0.738136 + 0.536287i 0.892127 0.451785i \(-0.149213\pi\)
−0.153991 + 0.988072i \(0.549213\pi\)
\(824\) −6.35392 −0.221349
\(825\) 0 0
\(826\) −6.16139 −0.214382
\(827\) 4.48139 + 3.25592i 0.155833 + 0.113219i 0.662969 0.748647i \(-0.269296\pi\)
−0.507136 + 0.861866i \(0.669296\pi\)
\(828\) 0 0
\(829\) 5.71784 + 17.5977i 0.198589 + 0.611194i 0.999916 + 0.0129672i \(0.00412771\pi\)
−0.801327 + 0.598227i \(0.795872\pi\)
\(830\) −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 −0.808337 0.588719i \(-0.799632\pi\)
0.999999 0.00115518i \(-0.000367705\pi\)
\(840\) 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 −0.902930 0.429788i \(-0.858588\pi\)
0.129732 + 0.991549i \(0.458588\pi\)
\(854\) 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 −0.384652 0.923062i \(-0.625678\pi\)
0.759020 + 0.651067i \(0.225678\pi\)
\(864\) 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 −0.564262 0.825596i \(-0.690839\pi\)
0.941771 0.336256i \(-0.109161\pi\)
\(878\) 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 0.786354 + 0.617776i \(0.211966\pi\)
−0.999293 + 0.0375844i \(0.988034\pi\)
\(884\) 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 0.968163 + 0.250320i \(0.0805357\pi\)
−0.636126 + 0.771585i \(0.719464\pi\)
\(888\) 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 0.317677 0.948199i \(-0.397097\pi\)
0.999958 0.00911935i \(-0.00290282\pi\)
\(908\) −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 0.228549 0.973532i \(-0.426602\pi\)
−0.855259 + 0.518201i \(0.826602\pi\)
\(912\) 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 −0.481749 0.876309i \(-0.659998\pi\)
0.684551 + 0.728965i \(0.259998\pi\)
\(920\) −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 −0.767450 0.641109i \(-0.778475\pi\)
0.372576 + 0.928002i \(0.378475\pi\)
\(930\) 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 0.326797 0.945095i \(-0.394031\pi\)
−0.797853 + 0.602853i \(0.794031\pi\)
\(938\) 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 0.140090 0.990139i \(-0.455261\pi\)
0.984968 + 0.172737i \(0.0552609\pi\)
\(942\) 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 0.996844 + 0.0793863i \(0.0252960\pi\)
−0.759802 + 0.650155i \(0.774704\pi\)
\(954\) 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 −0.995183 0.0980383i \(-0.968743\pi\)
0.862745 + 0.505639i \(0.168743\pi\)
\(972\) 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 0.466392 0.884578i \(-0.345554\pi\)
−0.697161 + 0.716915i \(0.745554\pi\)
\(978\) 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 0.999120 0.0419459i \(-0.0133557\pi\)
−0.832960 + 0.553333i \(0.813356\pi\)
\(984\) 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 0.933929 0.357459i \(-0.116357\pi\)
−0.965673 + 0.259759i \(0.916357\pi\)
\(998\) 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.730.4 36
3.2 odd 2 891.2.f.f.730.6 36
9.2 odd 6 99.2.m.b.4.6 72
9.4 even 3 297.2.n.b.235.6 72
9.5 odd 6 99.2.m.b.70.4 yes 72
9.7 even 3 297.2.n.b.37.4 72
11.3 even 5 inner 891.2.f.e.487.4 36
11.5 even 5 9801.2.a.cp.1.11 18
11.6 odd 10 9801.2.a.cn.1.8 18
33.5 odd 10 9801.2.a.cm.1.8 18
33.14 odd 10 891.2.f.f.487.6 36
33.17 even 10 9801.2.a.co.1.11 18
99.5 odd 30 1089.2.e.p.727.11 36
99.14 odd 30 99.2.m.b.25.6 yes 72
99.25 even 15 297.2.n.b.91.6 72
99.38 odd 30 1089.2.e.p.364.11 36
99.47 odd 30 99.2.m.b.58.4 yes 72
99.50 even 30 1089.2.e.o.727.8 36
99.58 even 15 297.2.n.b.289.4 72
99.83 even 30 1089.2.e.o.364.8 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.6 72 9.2 odd 6
99.2.m.b.25.6 yes 72 99.14 odd 30
99.2.m.b.58.4 yes 72 99.47 odd 30
99.2.m.b.70.4 yes 72 9.5 odd 6
297.2.n.b.37.4 72 9.7 even 3
297.2.n.b.91.6 72 99.25 even 15
297.2.n.b.235.6 72 9.4 even 3
297.2.n.b.289.4 72 99.58 even 15
891.2.f.e.487.4 36 11.3 even 5 inner
891.2.f.e.730.4 36 1.1 even 1 trivial
891.2.f.f.487.6 36 33.14 odd 10
891.2.f.f.730.6 36 3.2 odd 2
1089.2.e.o.364.8 36 99.83 even 30
1089.2.e.o.727.8 36 99.50 even 30
1089.2.e.p.364.11 36 99.38 odd 30
1089.2.e.p.727.11 36 99.5 odd 30
9801.2.a.cm.1.8 18 33.5 odd 10
9801.2.a.cn.1.8 18 11.6 odd 10
9801.2.a.co.1.11 18 33.17 even 10
9801.2.a.cp.1.11 18 11.5 even 5